Hypothesis Testing in Statistics, Exams of Mathematics

Download Hypothesis Testing in Statistics and more Exams Mathematics in PDF only on Docsity! MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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 MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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. That is correct! MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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 right- tailed tests are: • H0:X≤7.4, Ha:X>7.4 • H0:X≤3.8, Ha:X>3.8 Question 3 1/1 points Find the Type II error given that the null hypothesis, H0, is: a building inspector claims that no more than 15% of structures in the county were built without permits. That is correct! The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, no more than 15% of the structures really were built without permits. The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures really were built without permits. The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, at most 15% of the structures were built without permits. The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures were built without permits. Answer Explanation Correct answer: The building inspector thinks that no more than 15% of the structures in the county MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 were built without permits when, in fact, more than 15% of the structures were built without permits. A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In this case, the Type II error is when the building inspector thinks that no more than 15% of the MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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 Questions & Answers (Version 1 & 2)2024/2025 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: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 Questions & Answers (Version 1 & 2)2024/2025 Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. Reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. 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: Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. In making the decision to reject or not reject H0, if α>p-value, reject H0 because the results of the sample data are significant. There is sufficient evidence to conclude that H0 is an incorrect belief and that the alternative hypothesis, Ha, may be correct. If α≤p- value, do not reject H0. The results of the sample data are not significant, so there is not sufficient evidence to conclude that the alternative hypothesis, Ha, may be correct. In this case, α=0.04 is less than or equal to p=0.0401, so the decision is to not reject the null hypothesis. • • • QUESTION 7 1/1 POINTS A recent study suggested that 81% of senior citizens take at least one prescription medication. Amelia is a nurse at a large hospital who would like to know whether the percentage is the same for senior citizen patients who go to her hospital. She randomly selects 59 senior citizens patients who were treated at the hospital and finds that 49 of them take at least one prescription medication. What are the null and alternative hypotheses for this hypothesis test? That is correct! MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 {H0:p=0.81Ha:p>0.81 {H0:p≠0.81Ha:p=0.81 {H0:p=0.81Ha:p<0.81 {H0:p=0.81Ha:p≠0.81 Answer Explanation Correct answer: {H0:p=0.81Ha:p≠0.81 First verify whether all of the conditions have been met. Let p be the population proportion for the senior citizen patients treated at Amelia's hospital who take at least one prescription medication. 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 MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 H0:p = 0.12 MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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: 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 Questions & Answers (Version 1 & 2)2024/2025 • $\text{P-value=}0.124$P-value=0.124 Here are the steps needed to calculate the p-value for a hypothesis test for a proportion: MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 data with the level of significance. MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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. QUESTION 11 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%. MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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 MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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 Questions & Answers (Version 1 & 2)2024/2025 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 Questions & Answers (Version 1 & 2)2024/2025 That is correct! 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. MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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 Questions & Answers (Version 1 & 2)2024/2025 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 Questions & Answers (Version 1 & 2)2024/2025 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 estimate, a predicted time of 31.85 minutes, is both reliable and reasonable. 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? MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 Population change can be positive or negative, and it can increase or decrease. Based on the given information, there are no practical limits to population change, although there are limits such as the decrease in population cannot exceed the current population (as it would leave a MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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 Questions & Answers (Version 1 & 2)2024/2025 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 Questions & Answers (Version 1 & 2)2024/2025 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 study is an observational study. 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 MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 1/1 POINTS MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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. MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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 Questions & Answers (Version 1 & 2)2024/2025 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 $$33 $ $ Answer Explanation MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 Lower Class Limit Upper Class Limit Fr 1$$ 2$$ 3 $ 4$$ 5$$ 6 $ 7$$ 8$$ 9 $ 10$$ 11$$ 1 2 Correct answers: • 1$10$10 • 2$15$15 • 3$6$6 • 4$16$16 • 5$21$21 • 6$7$7 • 7$22$22 • 8$27$27 • 9$4$4 • 10$28$28 • 11$33$33 • 12$3$3 Note that the data is not ordered and that we have been asked to use 4 classes. To determine the class width, use the formula: Max Value−Min ValueNumber of Classes=31−104=5.25. Since this value is not an integer, round to 6. MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 A histogram has a vertical axis labeled Frequency and has a horizontal axis that measures six categories of rainbow trout weight (in pounds). Reading from left-to-right, the weight and frequency of each category are: 4.5 to 6.5 has frequency of 4, 6.5 to 8.5 has frequency 5, 8.5 to 10.5 has frequency 7, 10.5 to 12.5 has frequency 3, 12.5 to 14.5 has frequency 1, 14.5 to 16.5 has frequency 2. That is correct! $$greater than 12.5 but less than 14.5 Answer Explanation Correct answers: MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 • $\text{greater than }12.5\ \text{but less than }14.5$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 Questions & Answers (Version 1 & 2)2024/2025 MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 • $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 Questions & Answers (Version 1 & 2)2024/2025 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. MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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 Questions & Answers (Version 1 & 2)2024/2025 5 2 MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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. MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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 Questions & Answers (Version 1 & 2)2024/2025 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. MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is short and the most spread out, curve Upper B is tall and the least spread out, and curve C is farther to the left than A. That is correct! A B C Answer Explanation MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 Correct answer: MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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 MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 1/1 POINTS MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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 MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 $$(67, 87) Answer Explanation Correct answers: • $\left(67,\ 87\right)$(67, 87) A confidence interval is an interval of values, centered on a point estimate, of the form (pointestimate−marginof error,pointestimate+marginof error) Using the given point estimate for the mean, x¯=77 and margin of error 10, the confidence interval is: (77−10,77+10)(67,87) QUESTION 38 1/1 POINTS A random sample of adults were asked whether they prefer reading an e-book over a printed book. The survey resulted in a sample proportion of p′=0.14, with a sampling standard deviation of σp′=0.02, who preferred reading an e-book. Use the empirical rule to construct a 95% confidence interval for the true proportion of adults who prefer e-books. That is correct! $$(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)(0.10,0.18) MATH 225N Week 8 Final Exam Questions & Answers (Version 1 & 2)2024/2025 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 Questions & Answers (Version 1 & 2)2024/2025 That's not right. • Value Frequency 5 1 6 2 7 10 8 11 9 17 10 17 11 15 12 12 MATH 225N Week 8 Final Exam (Version 1 & 2) 16 1 14 3 15 1 MATH 225N Week 8 Final Exam (Version 1 & 2) 16 1 • • 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) 16 1 • • 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 Frequenc y 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 Frequenc y 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) 7 8 8 10 9 13 10 26 11 14 12 12 13 8 14 3 15 1 16 1 The data in this table is roughly symmetrical about 10. Value Frequency MATH 225N Week 8 Final Exam (Version 1 & 2) That is correct! 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) True False Answer Explanation Correct answer: False In supply and demand, a company doesn't make a product hoping that someone will buy them, they have a Demand first for their product and then, they produce more of that given product. 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. StudentsplaysportsdonotplaysportsTotalplayaninstrument33donotplayaninstrument69Total6267 That is correct! $$34 Answer Explanation Correct answers: • $34$34 MATH 225N Week 8 Final Exam (Version 1 & 2) 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: StudentsplaysportsdonotplaysportsTotalplayaninstrument273360donotplayaninstrument 353469T otal6267129 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 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. StudentsplaysportsdonotplaysportsTotalplayaninstrument33donotplayaninstrument69Total6267 That is correct! 34$$ 34 - correct 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: StudentsplaysportsdonotplaysportsTotalplayaninstrument273360donotplayaninstrument 353469T otal6267129 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 •