Hypothesis Testing in Statistics, Exams of Mathematics

Download Hypothesis Testing in Statistics and more Exams Mathematics in PDF only on Docsity! Page 1 MATH 225N FINAL EXAM 2020 – CHAMBERLAIN COLLEGE OF NURSING (GRADE A) 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: ≠33μ ; Ha: =33μ H0: =33μ ; Ha: ≠33μ H0: ≥33μ ; Ha: <33μ H0: ≤33μ ; Ha: >33μ Answer Explanation Correct answer: 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 Page 1 of 89 H0: =33μ ; Ha: ≠33μ Page 2 H0 is =33μ . The alternative hypothesis is contradictory to the null hypothesis, so Ha is ≠33μ . 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. That is correct!  H0:X≥17.1, Ha:X<17.1 H0:X=14.4, Ha:X≠14.4 H0:X≤3.8, Ha:X>3.8 H0:X≤7.4, Ha:X>7.4 H0:X=3.3, Ha:X≠3.3  Answer Explanation Correct answer: Page 2 of 89         H0:X≤3.8, Ha:X>3.8 H0:X≤7.4, Ha:X>7.4 Page 5 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, =0.5σ . 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¯−μ0 n√σ =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. 9650.9720.020.9360.9470.9570.9660.9730.030.9370.9480.9580.9660.9 730.040.9380.9490.9590.9670.9740.050.9390.9510.9600.9680.9740.06 0.9410.9520.9610.9690.9750.070.9420.9530.9620.9690.9760.080.9430. 9540.9620.9700.9760.090.9440.9540.9630.9710.977 That is correct! $$0.041 Answer Explanation Correct answers:  $0.041$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. Page 5 of 89 Page 6 A standard normal curve with two points labeled on the horizontal axis. The mean is labeled at 0.00 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: =8.2μ seconds; Ha: <8.2μ seconds  =0.04α (significance level)  z0=−1.75  p=0.0401 That is correct! Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level =0.04α . Page 6 of 89 Page 7 Reject the null hypothesis because the p-value 0.0401 is greater than the significance level =0.04α . Reject the null hypothesis because the value of z is negative. Reject the null hypothesis because |−1.75|>0.04. Do not reject the null hypothesis because |−1.75|>0.04. Answer Explanation Correct answer: Page 7 of 89 Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level =0.04α . Page 10 1. Since there are two independent outcomes for each trial, the proportion follows a binomial model. 2. The question states that the sample was collected randomly. 3. The expected number of successes, np=47.79, and the expected number of failures, nq=n(1−p)=11.21, are both greater than or equal to 5. Since Amelia is testing whether the proportion is the same, the null hypothesis is that p is equal to 0.81 and the alternative hypothesis is that p is not equal to 0.81. The null and alternative hypotheses are shown below. {H0:p=0.81Ha:p≠0.81 QUESTION 8 1/1 POINTS 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 Page 10 of 89 Page 11 p^=951000=0.095. The test statistic is calculated as follows: Page 11 of 89 Page 12 z=p^−p0p0 (1−p⋅ 0)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 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: Page 12 of 89 z 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 That is correct! Page 15 To come to a conclusion and interpret the results for a hypothesis test for proportion using the P-Value Approach, the first step is to compare the p- value from the sample data with the level of significance. The decision criteria is then as follows: If the p-value is less than or equal to the given significance level, then the null hypothesis should be rejected. So, if p≤α, reject H0; otherwise fail to reject H0. When we have made a decision about the null hypothesis, it is important to write a thoughtful conclusion about the hypotheses in terms of the given problem's scenario. Assuming the claim is the null hypothesis, the conclusion is then one of the following:  if the decision is to reject the null hypothesis, then the conclusion is that there is enough evidence to reject the claim.  if the decision is to fail to reject the null hypothesis, then the conclusion is that there is not enough evidence to reject the claim. Assuming the claim is the alternative hypothesis, the conclusion is then one of the following:  if the decision is to reject the null hypothesis, then the conclusion is that there is enough evidence to support the claim.  if the decision is to fail to reject the null hypothesis, then the conclusion is that there is not enough evidence to support the claim. In this example, the p-value = 0.026. We then compare the p-value to the level of significance to come to a conclusion for the hypothesis test. In this example, the p-value is less than the level of significance which is 0.05. Since the p-value is greater than the level of significance, the conclusion is to reject the null hypothesis . Page 15 of 89 Page 16 QUESTION 11 Page 16 of 89 Page 17 1/1 POINTS Becky's statistics teacher was teaching the class how to perform the z-test for a proportion. Becky was bored because she had already mastered the test, so she decided to see if the coin she had in her pocket would come up heads or tails in a truly random fashion when flipped. She discretely flipped the coin 30 times and got heads 18 times. Becky conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of heads is different from 50%. 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- Page 17 of 89 Page 20 Page 20 of 89 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. Page 21 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 That is correct! Page 21 of 89 Page 22 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. Page 22 of 89 Page 25 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 Page 25 of 89 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. Page 26 strong linear relationship between the variables. Page 26 of 89 Page 27 Video Games (Minutes) 306090120 Time with Family (Minutes) 504035 25 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? That is correct! The estimate, a predicted time of 31.85 minutes, is unreliable but reasonable. The estimate, a predicted time of 31.85 minutes, is both unreliable and unreasonable. The estimate, a predicted time of 31.85 minutes, is both reliable and reasonable. The estimate, a predicted time of 31.85 minutes, is reliable but unreasonable. Answer Explanation Correct answer: The data in the table only includes video game times between 30 and 120 minutes, so the line of best fit gives reasonable predictions for values of x between 30 and 120. Since 95 is between these values, the estimate is both reliable and reasonable. QUESTION 15 0/1 POINTS Which of the following are feasible equations of a least squares regression line for the annual population change of a small country from the year 2000 to the year 2015? Select all that apply. Page 27 of 89 The estimate, a predicted time of 31.85 minutes, is both reliable and reasonable. Page 30 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. 1.1 1380 0.4 556 1.0 771 0.5 304 1.4 532 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 Page 30 of 89 B-V index Distance (ly) Page 31 the built-in CORREL function. Page 31 of 89 Page 32 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 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. 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 Page 32 of 89 Weight Mileage Page 35 1/1 POINTS A farmer divided his piece of land into 4 equivalent groups. The quality of the soil is the same across the 4 groups of land. He planted the same crop in all 4 groups of land and recorded the yield of the crop in all 4 groups for a 4 week period. Is the study observational or experimental? If it is an experiment, what is the controlled factor? That is correct! The study is an observational study. The study is an experiment. The controlled factor is the 4 week observation period. The study is an experiment. The controlled factor is the land. The study is an experiment. The controlled factor is the growth of the crops. Answer Explanation Correct answer: The samples are chosen using an appropriate process; however, no attempt is made to control any aspect of the sample even though the variables of interest are recorded for each group. QUESTION 20 1/1 POINTS 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? Page 35 of 89 The study is an observational study. Page 36 That is correct! the physicians Page 36 of 89 Page 37 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: 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 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! nomin al ordinal interv al ratio Answer Explanation Correct answer: Page 37 of 89 the group that received the drug with no therapeutic effect Page 40 Correct answers: Note that the data is not ordered and that we have been asked to use 4 classes. To determine the class width, use the formula: Max Value−Min ValueNumber of Classes=31−104=5.25. Since this value is not an integer, round to 6. Use the minimum value, 10, for the lower class limit of the first class. To find all other lower class limits, add the class width, 6. For example, the second lower class limit would be: 10+6=16. Page 40 of 89 Lower Class Limit Upper Class Limit 1$$ 2$$ 4$$ 5$$ 7$$ 8$$ 10$$ 11$$ 1$10$10 2$15$15 3$6$6 4$16$16 5$21$21 6$7$7 7$22$22 8$27$27 9$4$4 10$28$28 11$33$33 12$3$3 Page 41 Lower Class Limit Upper Class Limit Frequency 10 16 22 28 To find the upper class limits, add the class width minus 1, to each lower class limit. For example, the upper class limit of the first class would be: 10+5=15. Lower Class Limit Upper Class Limit Frequency 10 15 16 21 22 27 28 33 To find the frequency for each class, count the number of data values that fall within the range of each class. For example, the data values 15, 14, 10, 10, 14, and 10 fall within the range of the first class, 10-15. So, the frequency of this class is 6. Lower Class Limit Upper Class Limit Frequency 10 15 6 16 21 7 22 27 4 28 33 3 QUESTION 23 1/1 POINTS The histogram below displays the weights of rainbow trout (in pounds) caught by all visitors at a lake on a Saturday afternoon. According to this histogram, which range of weights (in pounds) contains the lowest Page 41 of 89 Page 42 frequency? Page 42 of 89 Page 45 Answer Explanation Correct answer: Page 45 of 89 Page 46 uniform All the bars in a uniform histogram are about the same height. QUESTION 25 1/1 POINTS The bar graph below shows the number of boys and girls in different classes. A bar graph has a horizontal axis labeled Classes and a vertical axis labeled Students from 0 to 16 in increments of 2. There are two vertical bars above each horizontal axis label, with the bar on the left representing Boys and the bar on the right representing Girls. The bars have heights as follows, with the horizontal axis label listed first and the bar heights listed second from left to right: Mrs. Brown, 10 and 15; Ms. James, 11 and 12. How many total students are in Ms. James's class? Do not include the units in your answer. Page 46 of 89 Page 47 That is correct! $$23 Answer Explanation Correct answers:  $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? Page 47 of 89 Page 50 From the data, when the square footage is between 8.5 and 10, the number of TVs remains the same. Answer Explanation Correct answer: 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: 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. 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! $$mean=16 boxes Answer Explanation Correct answers:  $\text{mean=}16\text{ boxes}$mean=16 boxes Page 50 of 89 From the data, when the square footage is between 8.5 and 10, the number of TVs From the data, there is a steady increase in the square footage and number Page 51 Remember that the mean is the sum of the numbers divided by the number of numbers. There are 5 numbers in the list. So we find that the mean boxes sold is QUESTION 28 1/1 POINTS Given the following list of prices (in thousands of dollars) of randomly selected trucks at a car dealership, find the median. 20,46,19,14,42,26,33 That is correct! $$median=26 thousands of dollars Answer Explanation Correct answers:  $\text{median=}26\text{ thousands of dollars}$median=26 thousands of dollars It helps to put the numbers in order. 14,19,20,26,33,42,46 Now, because the list has length 7, which is odd, we know the median number will be the middle number. In other words, we can count to item 4 in the list, which is 26. So the median price (in thousands of dollars) of randomly selected trucks at a car dealership is 26. QUESTION 29 1/1 POINTS Each person in a group shuffles a deck of cards and keeps selecting a card until a queen appears. Find the mode of the following number of cards drawn from a deck until a queen appears. 3,12,3,11,5,5,3,10,12 Page 51 of 89 That is correct! Page 52 Answer Explanation Correct answers:  $\text{mode=}3\text{ cards}$mode=3 cards If we count the number of times each value appears in the list, we get the following frequency table: Value Frequency 3 3 5 2 10 1 11 1 12 2 Note that 3 occurs 3 times, which is the greatest frequency, so 3 is the mode of the number of cards drawn from a deck until a queen appears. QUESTION 30 1/1 POINTS Given the following histogram, decide if the data is skewed or symmetrical. Page 52 of 89 $$mode=3 cards Page 55 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? 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 Page 55 of 89 Page 56 above the class label C has the following five-number summary: 60, 72, 75, 80, and 92. The box-and-whisker Page 56 of 89 Page 57 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 B C D Answer Explanation Correct answer: C Remember that the standard deviation is a measure of how spread out the data is. If the values are concentrated around the mean, then a data set has a lower standard deviation. A box and whisker plot with short whiskers and a short box has values that are less spread out, and hence has a smaller standard deviation. QUESTION 32 1/1 POINTS The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest standard deviation. Page 57 of 89 Page 60 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 Correct answer: 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! Page 60 of 89 At the 0.01 level of significance, the coin is likely not a fair coin. Page 61 True Page 61 of 89 Page 62 False Answer Explanation Correct answer: 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 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 Page 62 of 89 True Page 65 Answer Explanation Correct answers:  $\left(67,\ 87\right)$(67, 87) A confidence interval is an interval of values, centered on a point estimate, of the form (pointestimate−marginof error,pointestimate+marginof error) Using the given point estimate for the mean, x¯=77 and margin of error 10, the confidence interval is: (77−10,77+10)(67,87) QUESTION 38 1/1 POINTS A random sample of adults were asked whether they prefer reading an e- book over a printed book. The survey resulted in a sample proportion of p ′=0.14, with a sampling standard deviation of σp′=0.02, who preferred reading an e-book. Use the empirical rule to construct a 95% confidence interval for the true proportion of adults who prefer e-books. That is correct! $$(0.10, 0.18) Answer Explanation Correct answers:  $\left(0.10,\ 0.18\right)$(0.10, 0.18) By the Empirical Rule, a 95% confidence interval corresponds to a z-score of z=2. Substituting the given values p′=0.14 and σp′=0.02, a confidence interval is (p′−z⋅σp′,p′+z⋅σp′)(0.14−2 0.02,0.14+2 0.02)(0.14−0.04,0.14+0.04)⋅ ⋅ (0.10,0. Page 65 of 89 Page 66 18) Page 66 of 89 Page 67 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=z 2α =z0.025=1.96, because the confidence level is 95%. From the problem, we know that =3.7 σ 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=(z Eσ )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 · Page 67 of 89 Page 70 14 3 15 1 16 1 Value Frequency 12 1 13 1 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 7 2  Answer Explanation Correct answer: Page 70 of 89     Page 71 Value Frequency 12 1 13 1 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 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 Page 71 of 89 Page 72 18 19 Page 72 of 89 Page 75 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 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! the group that received the anxiety- reduction pill the psychological study all the people in the study the group that received the inert pill Page 75 of 89 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. Page 76 Answer Explanation Page 76 of 89 Page 77 Correct answer: 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 ≥38 μ and alternative hypothesis <38μ ? That is correct! 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: Consider each of the options. The scenario in option B has the null hypothesis ≥38 μ 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 Page 77 of 89 the group that received the inert pill A fitness center claims that the mean amount of time that a person spends at the gym per visit is fewer than 38 minutes. Page 80 that 33 added to the unknown number in the middle is 67, so that unknown number is 34. Continuing in this way, we can fill in the entire table: StudentsplaysportsdonotplaysportsTotalplayaninstrument273360donot playaninstrument353469Total6267129 From this, we can see that the number of students who both do not play sports and do not play an instrument is 34. FEEDBACK     Content attribution- Opens a dialog QUESTION 45 1/1 POINTS Fill in the following contingency table and find the number of students who both do not play sports AND do not play an instrument. StudentsplaysportsdonotplaysportsTotalplayaninstrument33donotplaya ninstrument69Total6267 That is correct! $$34 Answer Explanation Correct answers:  $34$34 By using the known totals along the rows and columns you can fill in the rest of the contingency table. For example, looking at the second row in the table, we know that 33 added to the unknown number in the middle is 67, so that unknown number is 34. Continuing in this way, we can fill in the entire table: Page 80 of 89 Page 81 StudentsplaysportsdonotplaysportsTotalplayaninstrument273360donot playaninstrument353469Total6267129 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 H0:X=13.2, Ha:X≠13.2 H0:X=17.8, Ha:X≠17.8  Page 81 of 89         Page 82 Answer Explanation Correct answer: 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! 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 Page 82 of 89 H0:X≥19.7, Ha:X<19.7 H0:X≥11.2, Ha:X<11.2 Page 85 Because A is shorter and more spread out than B, we find that A has the larger standard deviation. QUESTION 49 1/1 POINTS Hugo averages 72 words per minute on a typing test with a standard deviation of 12 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(72,12)∼ . Suppose Hugo types 54 words per minute in a typing test on Wednesday. The z-score when x=54 is . This z- score tells you that x=54 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 54 words per minute in a typing test on Wednesday. The z-score when x=54 is −1.2. This z-score tells you that x=54 is 1.2 standard deviations to the left of the mean, 72. Suppose Hugo types 54 words per minute in a typing test on Wednesday. The z-score when x=54 is 1.2. This z-score tells you that x=54 is 1.2 standard deviations to the right of the mean, 72. Suppose Hugo types 54 words per minute in a typing test on Wednesday. The z-score when x=54 is 1.5. This z-score tells you that x=54 is 1.5 standard deviations to the right of the mean, 72. Suppose Hugo types 54 words per minute in a typing test on Wednesday. Page 85 of 89 Page 86 The z-score when x=54 is −1.5. This z-score tells you that x=54 is 1.5 standard deviations to the left of the mean, 72. Answer Explanation Page 86 of 89 Page 87 Correct answer: The z-score can be found using the formula z=x− =54−7212=−1812≈−1.5μσ 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 =72μ 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 54 words per minute is 1.5 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 4 2 2 7 1 8 1 9 1 10 4 12 3 16 1 20 1 22 1 Page 87 of 89 Suppose Hugo types 54 words per minute in a typing test on Wednesday. The z-score when x=54 is −1.5. This z-score tells you that x=54 is 1.5 standard deviations to the left of the mean, 72.