MATH 225N Week 8 Final Exam Hypothesis Test Questions, Exams of Statistics

Download MATH 225N Week 8 Final Exam Hypothesis Test Questions and more Exams Statistics in PDF only on Docsity! MATH 225N Week 8 Final Exam (Version 1 & 2) MATH 225N Week 8 Final Exam Question 1 1/1 points A fitness center claims that the mean amount of time that a person spends at the gym per visit is 33 minutes. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ. That is correct! H0: μ≠33; Ha: μ=33 H0: μ=33; Ha: μ≠33 H0: μ≥33; Ha: μ<33 H0: μ≤33; Ha: μ>33 Answer Explanation Correct answer: H0: μ=33; Ha: μ≠33 Let the parameter μ be used to represent the mean. The null hypothesis is always stated with some form of equality: equal (=), greater than or equal to (≥), or less than or equal to (≤). Therefore, in this case, the null hypothesis H0 is μ=33. The alternative hypothesis is contradictory to the null hypothesis, so Ha is μ≠33. Question 2 1/1 points The answer choices below represent different hypothesis tests. Which of the choices are right- tailed tests? Select all correct answers. MATH 225N Week 8 Final Exam (Version 1 & 2) That is correct! MATH 225N Week 8 Final Exam (Version 1 & 2) structures were built without permits when, in fact, more than 15% of the structures were built without permits. • • • Question 4 1/1 points Suppose a chef claims that her meatball weight is less than 4 ounces, on average. Several of her customers do not believe her, so the chef decides to do a hypothesis test, at a 10% significance level, to persuade them. She cooks 14 meatballs. The mean weight of the sample meatballs is 3.7 ounces. The chef knows from experience that the standard deviation for her meatball weight is ounces. • H0: μ≥4; Ha: μ<4 • α=0.1 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? That is correct! Test statistic = minus 2 point 2 4$$ Test statistic = minus 2 point 2 4 - correct Answer Explanation Correct answers: • Test statistic = minus 2 point 2 4 $\text{Test statistic = }-2.24$ • MATH 225N Week 8 Final Exam (Version 1 & 2) The hypotheses were chosen, and the significance level was decided on, so the next step in hypothesis testing is to compute the test statistic. In this scenario, the sample mean weight, x¯=3.7. The sample the chef uses is 14 meatballs, so n=14. She knows the standard deviation of the meatballs, σ=0.5. Lastly, the chef is comparing the population mean weight to 4 ounces. So, this value (found in the null and alternative hypotheses) is μ0. Now we will substitute the values into the formula to compute the test statistic: z0=x¯−μ0σn√=3.7−40.514√≈−0.30.134≈−2.24 So, the test statistic for this hypothesis test is z0=−2.24. • • • • Question 5 1/1 points What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of z0=1.74? (Do not round your answer; compute your answer using a value from the table below.) z1.51.61.71.81.90.000.9330.9450.9550.9640.9710.010.9340.9460.9560.9650.9720.020.9360.947 0.9570.9660.9730.030.9370.9480.9580.9660.9730.040.9380.9490.9590.9670.9740.050.9390.951 0.9600.9680.9740.060.9410.9520.9610.9690.9750.070.9420.9530.9620.9690.9760.080.9430.954 0.9620.9700.9760.090.9440.9540.9630.9710.977 That is correct! 0 point 0 4 1$$ 0 point 0 4 1 - correct Answer Explanation Correct answers: • 0 point 0 4 1 $0.041$ • The p-value is the probability of an observed value of z=1.74 or greater if the null hypothesis is true, because this hypothesis test is right-tailed. This probability is equal to the area under the Standard Normal curve to the right of z=1.74. MATH 225N Week 8 Final Exam (Version 1 & 2) A standard normal curve with two points labeled on the horizontal axis. The mean is labeled at 0.0 and an observed value of 1.74 is labeled. The area under the curve and to the right of the observed value is shaded. Using the Standard Normal Table, we can see that the p-value is equal to 0.959, which is the area to the left of z=1.74. (Standard Normal Tables give areas to the left.) So, the p-value we're looking for is p=1−0.959=0.041. Question 6 1/1 points Kenneth, a competitor in cup stacking, claims that his average stacking time is 8.2 seconds. During a practice session, Kenneth has a sample stacking time mean of 7.8 seconds based on 11 trials. At the 4% significance level, does the data provide sufficient evidence to conclude that Kenneth's mean stacking time is less than 8.2 seconds? Accept or reject the hypothesis given the sample data below. • H0:μ=8.2 seconds; Ha:μ<8.2 seconds • α=0.04 (significance level) • z0=−1.75 • p=0.0401 That is correct! MATH 225N Week 8 Final Exam (Version 1 & 2) A researcher claims that the proportion of cars with manual transmission is less than 10%. To test this claim, a survey checked 1000 randomly selected cars. Of those cars, 95 had a manual transmission. The following is the setup for the hypothesis test: {H0:p=0.10Ha:p<0.10 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. That is correct! $$Test_Statistic=−0.53 Answer Explanation Correct answers: • $\text{Test_Statistic}=-0.53$Test_Statistic=−0.53 The proportion of successes is p^=951000=0.095. The test statistic is calculated as follows: z=p^−p0p0⋅(1−p0)n−−−−−−√ z=0.095−0.100.10⋅(1−0.10)1000−−−−−−−−√ z≈−0.53 QUESTION 9 1/1 POINTS A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects. . The following is the setup for this hypothesis test: H0:p = 0.12 MATH 225N Week 8 Final Exam (Version 1 & 2) Ha:p ≠ 0.12 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places. The following table can be utilized which provides areas under the Standard Normal Curve: That is correct! $$P-value=0.124 Answer Explanation Correct answers: • $\text{P-value=}0.124$P-value=0.124 Here are the steps needed to calculate the p-value for a hypothesis test for a proportion: 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.029 1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037 1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046 1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068 MATH 225N Week 8 Final Exam (Version 1 & 2) 1. Determine if the hypothesis test is left tailed, right tailed, or two tailed. 2. Compute the value of the test statistic. 3. If the hypothesis test is left tailed, the p-value will be the area under the standard normal curve to the left of the test statistic z0 If the test is right tailed, the p-value will be the area under the standard normal curve to the right of the test statistic z0 If the test is two tailed, the p-value will be the area to the left of −|z0| plus the area to the right of |z0| under the standard normal curve For this example, the test is a two tailed test and the test statistic, rounding to two decimal places, is z=0.1033−0.120.12(1−0.12)900−−−−−−−−−−−−√≈−1.54. Thus the p-value is the area under the Standard Normal curve to the left of a z-score of -1.54, plus the area under the Standard Normal curve to the right of a z-score of 1.54. From a lookup table of the area under the Standard Normal curve, the corresponding area is then 2(0.062) = 0.124. QUESTION 10 1/1 POINTS 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.029 1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037 1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046 1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068 MATH 225N Week 8 Final Exam (Version 1 & 2) Which answer choice shows the correct null and alternative hypotheses for this test? That is correct! H0:p=0.6; Ha:p>0.6, which is a right-tailed test. H0:p=0.5; Ha:p<0.5, which is a left-tailed test. H0:p=0.6; Ha:p≠0.6, which is a two-tailed test. H0:p=0.5; Ha:p≠0.5, which is a two-tailed test. Answer Explanation Correct answer: H0:p=0.5; Ha:p≠0.5, which is a two-tailed test. The null hypothesis should be true proportion: H0:p=0.5. Becky wants to know if the true proportion of heads is different from 0.5. This means that we just want to test if the proportion is not 0.5. So, the alternative hypothesis is Ha:p≠0.5, which is a two-tailed test. QUESTION 12 1/1 POINTS John owns a computer repair service. For each computer, he charges $50 plus $45 per hour of work. A linear equation that expresses the total amount of money John earns per computer MATH 225N Week 8 Final Exam (Version 1 & 2) is y=50+45x. What are the independent and dependent variables? What is the y-intercept and the slope? That is correct! The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer. John charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. John earns $45 for each hour he works, so the slope is 45. The independent variable (x) is the amount, in dollars, John earns for a computer. The dependent variable (y) is the amount of time John fixes a computer. John charges a one-time fee of $45 (this is when x=0), so the y-intercept is 45. John earns $50 for each hour he works, so the slope is 50. The independent variable (x) is the amount, in dollars, John earns for a computer. The dependent variable (y) is the amount of time John fixes a computer. John charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. John earns $45 for each hour he works, so the slope is 45. The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer. John charges a one-time fee of $45 (this is when x=0), so the y-intercept is 45. John earns $50 for each hour he works, so the slope is 50. MATH 225N Week 8 Final Exam (Version 1 & 2) Answer Explanation Correct answer: The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer. John charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. John earns $45 for each hour he works, so the slope is 45. The independent variable (x) is the amount of time John fixes a computer because it is the value that changes. He may work different amounts per computer, and his earnings are dependent on how many hours he works. This is why the amount, in dollars, John earns for a computer is the dependent variable (y). The y-intercept is 50 (b=50). This is his one-time fee. The slope is 45 (a=45). This is the increase for each hour he works. QUESTION 13 1/1 POINTS Ariana keeps track of the amount of time she studies and the score she gets on her quizzes. The data are shown in the table below. Which of the scatter plots below accurately records the data? Hours studying Quiz score 1 5 2 5 3 7 4 9 5 9 MATH 225N Week 8 Final Exam (Version 1 & 2) A scatterplot has a horizontal axis labeled Hours studying from 0 to 6 in increments of 1 and a vertical axis labeled Quiz score from 0 to 9 in increments of 1. The following points are plotted: left-parenthesis 1 comma 5 right-parentheses; left-parenthesis 2 comma 5 right-parentheses; left- parenthesis 3 comma 7 right-parentheses; left-parenthesis 4 comma 8 right-parentheses; left- parenthesis 5 comma 8 right-parentheses. MATH 225N Week 8 Final Exam (Version 1 & 2) A scatterplot has a horizontal axis labeled Hours studying from 0 to 6 in increments of 1 and a vertical axis labeled Quiz score from 0 to 12 in increments of 2. The following points are plotted: left-parenthesis 1 comma 5 right-parentheses; left-parenthesis 2 comma 5 right- parentheses; left- parenthesis 3 comma 8 right-parentheses; left-parenthesis 4 comma 8 right-parentheses; left- parenthesis 5 comma 11 right-parentheses. All values are approximate. Answer Explanation Correct answer: MATH 225N Week 8 Final Exam (Version 1 & 2) A scatterplot has a horizontal axis labeled Hours studying from 0 to 6 in increments of 1 and a vertical axis labeled Quiz score from 0 to 10 in increments of 2. The following points are plotted: left-parenthesis 1 comma 5 right-parentheses; left-parenthesis 2 comma 5 right- parentheses; left- parenthesis 3 comma 7 right-parentheses; left-parenthesis 4 comma 9 right-parentheses; left- parenthesis 5 comma 9 right-parentheses. All values are approximate. The values for hours studying correspond to x-values, and the values for quiz score correspond to y-values. Each row of the table of data corresponds to a point (x,y) plotted in the scatter plot. For example, the first row, 1,5, corresponds to the point (1,5). Doing this for every row in the table, we find the scatter plot should have points (1,5), (2,5), (3,7), (4,9), and (5,9). QUESTION 14 1/1 POINTS Data is collected on the relationship between time spent playing video games and time spent with family. The data is shown in the table and the line of best fit for the data is y^=−0.27x+57.5. Assume the line of best fit is significant and there is a strong linear relationship between the variables. Video Games (Minutes) 306090120 Time with Family (Minutes) 50403525 According to the line of best fit, the predicted number of minutes spent with family for someone who spent 95 minutes playing video games is 31.85. Is it reasonable to use this line of best fit to make the above prediction? MATH 225N Week 8 Final Exam (Version 1 & 2) negative number of people in the country), or the increase in population could be limited by other real-world factors (such as lack of space or legal immigration limits). Your answer: yˆ=38,000+2500x QUESTION 17 1/1 POINTS An amateur astronomer is researching statistical properties of known stars using a variety of databases. They collect the color index, or B−V index, and distance (in light years) from Earth for 30 stars. The color index of a star is the difference in the light absorption measured from the star using two different light filters (a B and a V filter). This then allows the scientist to know the star's temperature and a negative value means a hot blue star. A light year is the distance light can travel in 1 year, which is approximately 5.9 trillion miles. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets, rounding to two decimal places. index Distance (ly) 1.1 1380 0.4 556 1.0 771 0.5 304 1.4 532 MATH 225N Week 8 Final Exam (Version 1 & 2) 1.0 751 0.5 267 0.8 229 0.5 552 HelpCopy to ClipboardDownload CSV That is correct! $$r= 0.18 Answer Explanation Correct answers: • $\text{r= }0.18$r= 0.18 The correlation coefficient can be calculated easily with Excel using the built-in CORREL function. 1. Open the accompanying data set in Excel. 2. In an open cell, type "=CORREL(A2:A31,B2:B31)", and then hit ENTER. You could label the result of this cell by writing "Correlation coefficient" or "r" in an adjacent open cell. The correlation coefficient, rounded to two decimal places, is r≈0.18. QUESTION 18 0/1 POINTS MATH 225N Week 8 Final Exam (Version 1 & 2) The weight of a car can influence the mileage that the car can obtain. A random sample of 20 cars’ weights and mileage is collected. The table for the weight and mileage of the cars is given below. Use Excel to find the best fit linear regression equation, where weight is the explanatory variable. Round the slope and intercept to three decimal places. Weight Mileage 30.0 32.2 20.0 56.0 20.0 46.2 45.0 19.5 40.0 23.6 45.0 16.7 25.0 42.2 55.0 13.2 17.5 65.4 HelpCopy to ClipboardDownload CSV MATH 225N Week 8 Final Exam (Version 1 & 2) To test the effectiveness of a drug proposed to relieve symptoms of headache, physicians included participants for a study. They gave the drug to one group and a drug with no therapeutic effect to another group. Which group receives the placebo? That is correct! the physicians the group that received the drug for headache the group that received the drug with no therapeutic effect all of the people in the study Answer Explanation Correct answer: the group that received the drug with no therapeutic effect When the experimental units are people, applying treatments that should be inert can actually have effects. In this study, the drug with no therapeutic effects is the placebo, so the group that receives that drug receives the placebo. QUESTION 21 1/1 POINTS MATH 225N Week 8 Final Exam (Version 1 & 2) A doctor notes her patient's temperature in degrees Fahrenheit every hour to make sure the patient does not get a fever. What is the level of measurement of the data? That is correct! nominal ordinal interval ratio Answer Explanation Correct answer: interval This is interval data because degrees Fahrenheit is a numerical scale where differences are meaningful. However, because Fahrenheit does not have a true zero value, it is not ratio data. QUESTION 22 0/1 POINTS As a member of a marketing team, you have been tasked with determining the number of DVDs that people have rented over the past six months. You sample twenty adults and decide that the best display of data is a frequency table for grouped data. Construct this table using four classes. MATH 225N Week 8 Final Exam (Version 1 & 2) 15,31,28,19,14,18,28,19,10,19,10,24,14,18,24,27,10,18,16,23 That's not right. Lower Class Limit Upper Class Limit Fr $$10 $$15 $$ $$16 $$21 $$ $$22 $$27 $$ $$18 $$33 $$ Answer Explanation MATH 225N Week 8 Final Exam (Version 1 & 2) To find the frequency for each class, count the number of data values that fall within the range of each class. For example, the data values 15, 14, 10, 10, 14, and 10 fall within the range of the first class, 10-15. So, the frequency of this class is 6. Lower Class Limit Upper Class Limit Frequency 10 15 6 16 21 7 22 27 4 28 33 3 QUESTION 23 1/1 POINTS The histogram below displays the weights of rainbow trout (in pounds) caught by all visitors at a lake on a Saturday afternoon. According to this histogram, which range of weights (in pounds) contains the lowest frequency? MATH 225N Week 8 Final Exam (Version 1 & 2) A histogram has a vertical axis labeled Frequency and has a horizontal axis that measures six categories of rainbow trout weight (in pounds). Reading from left-to-right, the weight and frequency of each category are: 4.5 to 6.5 has frequency of 4, 6.5 to 8.5 has frequency 5, 8.5 to 10.5 has frequency 7, 10.5 to 12.5 has frequency 3, 12.5 to 14.5 has frequency 1, 14.5 to 16.5 has frequency 2. That is correct! $$greater than 12.5 but less than 14.5 Answer Explanation Correct answers: MATH 225N Week 8 Final Exam (Version 1 & 2) • $\text{greater than }12.5\ \text{but less than }14.5$greater than 12.5 but less than 14.5 The range 12.5−14.5 has the lowest bar in the histogram, which means that this range of values also has the lowest frequency. Therefore, 1 visitor caught a rainbow trout that weighed greater than 12.5 but less than 14.5 pounds. QUESTION 24 1/1 POINTS Describe the shape of the given histogram. A histogram has a horizontal axis from 0 to 16 in increments of 2 and a vertical axis labeled Frequency from 0 to 10 in increments of 2. The histogram contains vertical bars of width 1 starting at the horizontal axis value 0. The heights of the bars are as follows, where the left horizontal axis label is listed first and the frequency is listed second: 0, 0; 1, 0; 2, 6; 3, 6; 4, 7; 5, 6; 6, 6; 7, 6; 8, 7; 9, 6; 10, 6; 11, 6; 12, 6; 13, 7; 14, 0; 15, 0. That is correct! uniform unimodal and symmetric MATH 225N Week 8 Final Exam (Version 1 & 2) • $23$23 To find the number of students in Ms. James's class, find the heights of the bars for that class and add them. In this case, we find it is 11+12=23. QUESTION 26 0/1 POINTS The line graph shown below represents the number of TVs in a house by square footage (in hundreds of feet). According to the information above, which of the following is an appropriate analysis of square footage and TVs? A line graph has an x-axis labeled Square Footage (in hundreds of feet) in increments of one, and a y-axis labeled Number of TV's in increments of one. Beginning at the point start parentheses 6,2 end parentheses, a line increases to the point start parentheses 8.5,3 end parentheses. The line remains constant to the point start parentheses 10,3 end parentheses. The line then increases, passing through the point start parentheses 12,5 end parentheses and continues increasing until it reaches the point start parentheses 16,6 end parentheses. MATH 225N Week 8 Final Exam (Version 1 & 2) That's not right. From the data, the number of TVs doubled from a square footage of 8.5 and 10. From the data, there is a steady decrease in the square footage and number of TVs. From the data, there is a steady increase in the square footage and number of TVs. From the data, when the square footage is between 8.5 and 10, the number of TVs remains the same. Answer Explanation Correct answer: From the data, when the square footage is between 8.5 and 10, the number of TVs remains the same. Given the line graph, at a square footage of 8.5, the number of TVs is 3. At a square footage of 10, the number of TVs is also 3. Therefore, when the square footage is between 8.5 and 10, the number of TVs remains the same. Your answer: From the data, there is a steady increase in the square footage and number of TVs. This response is not correct. While most of the line is increasing, the number of TVs remains the same between a square footage of 8.5 and 10. MATH 225N Week 8 Final Exam (Version 1 & 2) QUESTION 27 1/1 POINTS Alice sells boxes of candy at the baseball game and wants to know the mean number of boxes she sells. The numbers for the games so far are listed below. 16,14,14,21,15 Find the mean boxes sold. That is correct! $$mean=16 boxes Answer Explanation Correct answers: • $\text{mean=}16\text{ boxes}$mean=16 boxes Remember that the mean is the sum of the numbers divided by the number of numbers. There are 5 numbers in the list. So we find that the mean boxes sold is QUESTION 28 1/1 POINTS Given the following list of prices (in thousands of dollars) of randomly selected trucks at a car dealership, find the median. 20,46,19,14,42,26,33 That is correct! $$median=26 thousands of dollars Answer Explanation MATH 225N Week 8 Final Exam (Version 1 & 2) A bar graph has a horizontal axis titled Values labeled from 2 to 18 in increments of 2 and a vertical axis titled Frequency labeled from 0 to 200 in increments of 50. 14 bars are plotted, above the numbers 2 to 16. From left to right, the heights of the bars are as follows: 1. 5. 10. 40, 75, 125, 190, 180, 130, 125, 60, 25,20, 10. All values are approximate. That is correct! The data are skewed to the left. MATH 225N Week 8 Final Exam (Version 1 & 2) The data are skewed to the right. The data are symmetric. Answer Explanation Correct answer: The data are symmetric. Note that the histogram appears to be roughly symmetric. So the data are symmetric. QUESTION 31 1/1 POINTS Which of the data sets represented by the following box and whisker plots has the smallest standard deviation? MATH 225N Week 8 Final Exam (Version 1 & 2) Four horizontal box-and-whisker plots share a vertical axis with the classes D, C, B, and A and a horizontal axis from 0 to 120 in increments of 20. The box-and-whisker plot above the class label A has the following five-number summary: 44, 69, 77, 82, and 112. The box-and-whisker plot above the class label B has the following five-number summary: 19, 64, 78, 87, and 121. The box-and-whisker plot above the class label C has the following five-number summary: 60, 72, 75, 80, and 92. The box-and-whisker plot above the class label D has the following five- number summary: 2, 63, 77, 92, and 138. All values are approximate. That is correct! A MATH 225N Week 8 Final Exam (Version 1 & 2) B Remember that the standard deviation tells how spread out the normal distribution is. So a high standard deviation means the graph will be short and spread out. A low standard deviation means the graph will be tall and skinny. The distribution that is the tallest and least spread out is B, so that has the smallest standard deviation. QUESTION 33 1/1 POINTS Brayden tosses a coin 500 times. Of those 500 times, he observes heads a total of 416 times. Calculations show that the probability of this occurring by chance is less than 0.01, assuming the coin is fair. Determine the meaning of the significance level. That is correct! We expect that 416 of every 500 coin tosses will result in heads. At the 0.01 level of significance, the coin is likely not a fair coin. There is certainty that the coin is not a fair coin. The results are not statistically significant at the 0.05 level of significance. Answer Explanation MATH 225N Week 8 Final Exam (Version 1 & 2) Correct answer: At the 0.01 level of significance, the coin is likely not a fair coin. The results of the experiment are significant at the 0.01 level of significance. This means the probability that the outcome was the result of chance is 0.01 or less. Because of this, we can be fairly confident, but not certain, that the coin is not a fair coin. QUESTION 34 1/1 POINTS Is the statement below true or false? Independent is the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs. That is correct! True False Answer Explanation Correct answer: True Independent is defined as the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs. QUESTION 35 1/1 POINTS MATH 225N Week 8 Final Exam (Version 1 & 2) Of the following pairs of events, which pair has mutually exclusive events? That is correct! rolling a sum greater than 7 from two rolls of a standard die and rolling a 4 for the first throw drawing a 2 and drawing a 4 with replacement from a standard deck of cards rolling a sum of 9 from two rolls of a standard die and rolling a 2 for the first roll drawing a red card and then drawing a black card with replacement from a standard deck of cards Answer Explanation Correct answer: rolling a sum of 9 from two rolls of a standard die and rolling a 2 for the first roll Mutually exclusive events are events that cannot occur together. In this case, rolling a sum of 9 from two rolls of a standard die and rolling 2 for the first roll are two events that cannot possibly occur together. QUESTION 36 1/1 POINTS Fill in the following contingency table and find the number of students who both go to the beach AND go to the mountains. MATH 225N Week 8 Final Exam (Version 1 & 2) QUESTION 39 1/1 POINTS The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken? z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576 Use the table above for the z-score, and be sure to round up to the nearest integer. That is correct! $$14 dog heights Answer Explanation Correct answers: • $14\text{ dog heights}$14 dog heights The formula for sample size is n=z2σ2EBM2. In this formula, z=zα2=z0.025=1.96, because the confidence level is 95%. From the problem, we know that σ=3.7 and EBM=2. Therefore, n=z2σ2EBM2=(1.96)2(3.7)222≈13.15. Use n=14 to ensure that the sample size is large enough. Also, the sample size formula shown above is sometimes written using an alternate format of n=(zσE)2. In this formula, E is used to denote margin of error and the entire parentheses is raised to the exponent 2. Therefore, the margin of error for the mean can be denoted by "EBM" or by "E". Either formula for the sample size can be used and these formulas are considered as equivalent. QUESTION 40 0/1 POINTS Which of the following frequency tables show a skewed data set? Select all answers that apply. MATH 225N Week 8 Final Exam (Version 1 & 2) That's not right. • Value Frequency 5 1 6 2 7 10 8 11 9 17 10 17 11 15 12 12 13 7 14 7 15 0 MATH 225N Week 8 Final Exam (Version 1 & 2) 16 1 • • Value Frequency 5 1 6 3 7 8 8 10 9 13 10 26 11 14 12 12 13 8 14 3 15 1 MATH 225N Week 8 Final Exam (Version 1 & 2) 14 3 15 6 16 23 17 29 18 19 19 15 20 3 Value Frequency 0 5 1 16 2 23 3 19 4 22 5 9 6 4 MATH 225N Week 8 Final Exam (Version 1 & 2) 7 2 Remember that data are left skewed if there is a main concentration of large values with several much smaller values. Similarly, right skewed data have a main concentration of small values with several much larger values. We can see that the following is left skewed because of the concentration of large values with many smaller values: Value Frequency 12 1 13 1 14 3 15 6 16 23 17 29 18 19 19 15 20 3 MATH 225N Week 8 Final Exam (Version 1 & 2) And the following is right skewed because of its concentration of small values with many larger values: Value Frequency 0 5 1 16 2 23 3 19 4 22 5 9 6 4 7 2 The other frequency tables are more balanced and symmetrical. Your answer: Value Frequency 5 1 6 3 MATH 225N Week 8 Final Exam (Version 1 & 2) More people from rural areas want the defending champions to win the game. Exactly 216 out of every 374 urban residents want the defending champions to win the game. The results are statistically significant at the 0.05 level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. The data is not statistically significant at the 0.05 level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. Answer Explanation Correct answer: The results are statistically significant at the 0.05 level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. The probability value calculated is 0.03. This is less than 0.05, so we conclude that the data are statistically significant in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. QUESTION 42 1/1 POINTS In a psychological study aimed at testing a drug that reduces anxiety, the researcher grouped the participants into 2 groups and gave the anxiety-reduction pill to one group and an inert pill to another group. Which group receives the placebo? That is correct! MATH 225N Week 8 Final Exam (Version 1 & 2) the group that received the anxiety-reduction pill the psychological study all the people in the study the group that received the inert pill Answer Explanation Correct answer: the group that received the inert pill When the experimental units are people, applying treatments that should be inert can actually have effects. So the group that received the inert pill received the placebo. QUESTION 43 1/1 POINTS Which of the following results in the null hypothesis μ≥38 and alternative hypothesis μ<38? That is correct! MATH 225N Week 8 Final Exam (Version 1 & 2) A fitness center claims that the mean amount of time that a person spends at the gym per visit is at most 38 minutes. A fitness center claims that the mean amount of time that a person spends at the gym per visit is fewer than 38 minutes. A fitness center claims that the mean amount of time that a person spends at the gym per visit is 38 minutes. A fitness center claims that the mean amount of time that a person spends at the gym per visit is more than 38 minutes. Answer Explanation Correct answer: A fitness center claims that the mean amount of time that a person spends at the gym per visit is fewer than 38 minutes. Consider each of the options. The scenario in option B has the null hypothesis μ≥38 based on the words "fewer than" and the fact that the null hypothesis is always stated with some form of equality. QUESTION 44 1/1 POINTS True or False: The more shoes a manufacturer makes, the more shoes they sell. That is correct! MATH 225N Week 8 Final Exam (Version 1 & 2) From this, we can see that the number of students who both do not play sports and do not play an instrument is 34. • • • • Question 46 · 1/1 points The answer choices below represent different hypothesis tests. Which of the choices are left- tailed tests? Select all correct answers. That is correct! • H0:X=17.3, Ha:X≠17.3 • • H0:X≥19.7, Ha:X<19.7 • • H0:X≥11.2, Ha:X<11.2 • • MATH 225N Week 8 Final Exam (Version 1 & 2) H0:X=13.2, Ha:X≠13.2 • • H0:X=17.8, Ha:X≠17.8 • Answer Explanation Correct answer: H0:X≥19.7, Ha:X<19.7 H0:X≥11.2, Ha:X<11.2 Remember the forms of the hypothesis tests. • Right-tailed: H0:X≤X0, Ha:X>X0. • Left-tailed: H0:X≥X0, Ha:X<X0. • Two-tailed: H0:X=X0, Ha:X≠X0. So in this case, the left-tailed tests are: • H0:X≥11.2, Ha:X<11.2 • H0:X≥19.7, Ha:X<19.7 • • • • Question 47 · 1/1 points Assume the null hypothesis, H0, is: Jacob earns enough money to afford a luxury apartment. Find the Type I error in this scenario. That is correct! MATH 225N Week 8 Final Exam (Version 1 & 2) Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does. Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does not. Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does not. Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does. Answer Explanation Correct answer: Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does. A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is when Jacob thinks he does not earn enough money when he really does. • • • • Question 48 · 1/1 points Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. MATH 225N Week 8 Final Exam (Version 1 & 2) • Question 49 · 1/1 points Hugo averages 62 words per minute on a typing test with a standard deviation of 8 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(62,8). Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is . This z-score tells you that x=56 is standard deviations to the (right/left) of the mean, . Correctly fill in the blanks in the statement above. That is correct! Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is 0.75. This z-score tells you that x=56 is 0.75 standard deviations to the right of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −0.75. This z-score tells you that x=56 is 0.75 standard deviations to the left of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is 0.545. This z-score tells you that x=56 is 0.545 standard deviations to the right of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −0.545. This z-score tells you that x=56 is 0.545 standard deviations to the left of the mean, 62. MATH 225N Week 8 Final Exam (Version 1 & 2) Answer Explanation Correct answer: Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −0.75. This z-score tells you that x=56 is 0.75 standard deviations to the left of the mean, 62. The z-score can be found using the formula z=x−μσ=56−628=−68≈−0.75 A negative value of z means that that the value is below (or to the left of) the mean, which was given in the problem as μ=62 words per minute in a typing test. The z-score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. So, typing 56 words per minute is 0.75 standard deviations away from the mean. • • • • Question 50 · 1/1 points The following frequency table summarizes a set of data. What is the five-number summary? Value Frequency 1 6 2 2 3 1 4 1 8 1 9 1 10 1 16 6 20 3 21 1 23 1 24 1 25 1 27 1 MATH 225N Week 8 Final Exam (Version 1 & 2) That is correct! Min Q1 Median Q3 Max 1 2 16 20 27 Min Q1 Median Q3 Max 11 33 2020 2222 27 Min Q1 Median Q3 Max $_1$_ $_2$_ $_6$_ $_20$_ $_27$_ Min Q1 Median Q3 Max $_1$_ $_4$_ $_5$_ $_16$_ $_27$_ Min Q1 Median Q3 Max $_1$_ $_7$_ $_8$_ $_22$_ $_27$_ Answer Explanation Correct answer: Min Q1 Median Q3 Max $_1$_ $_2$_ $_16$_ $_20$_ $_27$_ We can immediately see that the minimum value is $_1$_ and the maximum value is $_27$_. If we add up the frequencies in the table, we see that there are $_27$_ total values in the data set. Therefore, the median value is the one where there are $_13$_ values below it and $_13$_ values above it. By adding up frequencies, we see that this happens at the value $_16$_, so that is the median. Now, looking at the lower half of the data, there are $_13$_ values there, and so the median value of that half of the data is $_2$_. This is the first quartile. Similarly, the third quartile is the median of the upper half of the data, which is $_20$_. $_\color{blue}{1}$_, $_1$_, $_1$_, $_1$_, $_1$_, $_1$_, $_\color{blue}{2}$_, $_2$_, $_3$_, $_4$_, $_8$_, $_9$_, $_10$_, $_\color{blue}{16}$_, $_16$_, $_16$_, $_16$_, $_16$_, $_16$_, $_20$_, $_\color{blue}{20}$_, $_20$_, $_21$_, $_23$_, $_24$_, $_25$_,