Instructor: Doug Ensley Course: MAT Applied Statistics - Ensley

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1 Student: Date: Instructor: Doug Ensley Course: MAT Applied Statistics - Ensley Assignment: Online 17 - Section To determine what students at a school would be willing to do to help address global warming, researchers take a random sample of 100 students. The students answer the questions, "How high of a tax would you be willing to add to gasoline (per gallon) in order to encourage drivers to drive less or to drive more fuel-efficient cars?" and, "Do you believe (yes or no) that global warming is a serious issue that requires immediate action?" The researchers want to compare the mean response on gasoline taxes (the first question) for those who answer yes and for those who answer no to the second question. Complete parts a through c below. a. Identify the response variable and the explanatory variable. What is the response variable? A. The fuel efficiency of the cars. B. The amount of tax the student is willing to add to a gallon of gasoline. C. Whether the student believes that global warming is a serious issue or not. D. Whether the person in the sample is a student at your school or not. What is the explanatory variable? A. The fuel efficiency of the cars. B. The amount of tax the student is willing to add to a gallon of gasoline. C. Whether the student believes that global warming is a serious issue or not. D. Whether the person in the sample is a student at your school or not. b. Are the two groups being compared independent samples or dependent samples? Why? The groups are (1) because the subjects are assigned to a group according to their response to the question about whether (2) c. Identify a confidence interval to use to compare the groups, specifying the parameters used in the comparison. If x 1 and x 2 are the sample mean response on gasoline taxes for the group who responded yes to the second question and the group who responded no, respectively, which of the expressions below produce a confidence interval to compare the groups? Select all that apply. A. ( x 1 x 2 ) ± t α / 2 (se) B. ( x 2 x 1 ) ± t α / 2 (se) C. x 1 + x 2 2 ± t α / 2 (se) D. x 2 x 1 2 ± t α / 2 (se) (1) independent dependent (2) they are willing to add taxes to gasoline. global warming is a serious issue. ID: of 8

2 2. Do women tend to spend more time on housework than men? If so, how much more? A study reported the results shown in the table to the right for the number of hours spent on housework per week. Complete parts a through d below. Housework Hours Gender Sample Size Mean Standard Deviation Women Men a. Based on this study, calculate how many more hours per week, on the average, women spend on housework than men. On average, women spend more hours per week on housework. b. Find the standard error for comparing the means. What factor causes the standard error to be small compared to the sample standard deviations for the two groups? The standard error is se =. (Round to four decimal places as needed.) The (1) groups. cause the standard error to be small compared to the sample standard deviations for the two c. Calculate the 95% confidence interval comparing the population means for women ( μ W ) and men ( μ M ). Interpret the result including the relevance of 0 being within the interval or not. The 95% confidence interval for ( μ W μ M ) is from to. (Round to two decimal places as needed.) The values in the 95% confidence interval (2) which implies that the population mean for women (3) the population mean for men. d. State the assumptions upon which the interval in part c is based. Upon which assumptions below is the interval based? Select all that apply. A. The samples from the two groups are independent. B. The standard deviations of the two populations are approximately equal. C. The population distribution for each group is approximately normal. D. The samples from the two groups are random. (1) nearly equal sample standard deviations nearly equal sample means large population sizes large sample sizes (2) include 0, are greater than 0, are less than 0, (3) is less than could be the same as is greater than ID: T 2 of 8

3 3. A study evaluated the weekly time (in hours) that men and women spent in employment. Software shows the result. Complete parts (a) through (d). 1 Click the icon to view the results. a. Does it seem plausible that employment has a normal distribution for each gender? A. It may or may not be plausible, depending on full data about each gender. B. It does not seem plausible that employment has a normal distribution for each gender because the lowest possible value is 0 and the standard deviations are about the same size as the means, an indication of skew. C. It seems plausible that employment has a normal distribution for each gender because the sample size is very large for each gender. b. What effect does the answer to (a) have on inferences comparing population means? What assumptions are made for the inferences in this table? A. One of the assumptions for this inference is a normal population distribution. The inference is likely affected because the population mean distribution depends on the population distribution. B. One of the assumptions for this inference is a normal population distribution. The inference is likely affected because the two-sided test for comparing two population means relies on the assumption of a normal population distribution. C. One of the assumptions for this inference is a normal population distribution. The inference is not likely affected because the sample size is very large and the two-sided test is robust with respect to that assumption. c. Explain how to interpret the confidence interval. A. We can be 95% confident that the population mean gender difference μmen μwomen in weekly time spent in employment is between and hours. B. We can be 5% confident that the population mean gender difference μmen μwomen in weekly time spent in employment is between and hours. C. We can be 95% confident that the population mean gender difference μmen μwomen in weekly time spent in employment is negative. d. Refer to (c). Do you think that the population means are equal? No. The population means are not likely equal because 0 does not fall in that range, indicating that there is a difference between genders in the population means with respect to time spent in employment. It appears that men spent more time in employment (on average) than women. Yes. The population means are likely equal because the range of the confidence interval is very small, indicating that there is not a difference between genders in the population means with respect to time spent in employment. 1: More Info Two-sample T for Employ Gender N Mean StDev SE Mean Men Women of 8 Difference = mu(men) mu(women) 95% CI for difference: ( 12.67, 14.33) T-Test of difference = 0 (vs not = ): T-value = P-value = 0.000

4 ID: A study of bulimia among college women studied the connection between childhood sexual abuse and a measure of family cohesion (the higher the score, the greater the cohesion). The sample mean on the family cohesion scale was 2.3 for 12 sexually abused students (s = 2.4) and 4.7 for 23 nonabused students (s = 3.5). a. Find the standard error for comparing the means. b. Construct a 95% confidence interval for the difference between the mean family cohesion for sexually abused students and non-abused students. Interpret. a. The standard error se =. (Round to four decimal places as needed.) b. The 95% confidence interval for the difference between the mean family cohesion for sexually abused students ( μ S ) and non-abused students ( μ N ). Interpret. The 95% confidence interval for ( μ S μ N ) is from to. (Round to two decimal places as needed.) The values in the 95% confidence interval (1) which implies that the population mean for sexually abused students (2) (1) are greater than 0, include 0, are less than 0, the population mean for nonabused students. (2) is greater than could be the same as is less than ID: T 4 of 8

5 5. When a survey asked, "About how many hours per week do you spend on ?", the results for those age 21 or under were as shown below. Answer parts (a) through (c). 2 Click the icon to view the table. a. Using software or a calculator, find the sample mean and standard deviation for each group. Interpret. Find the sample mean for the males x 1. x 1 = Find the sample mean for the females x 2. x 2 = Find the standard deviation for the males s 1. s 1 = Find the standard deviation for the females s 2. s 2 = Interpret these values. A. The sample mean time was slightly higher for females, but notice the outlier for the female group. The data was more variable for males, but this may also merely reflect the outlier. B. The sample mean time was slightly higher for females, but notice the outlier for the female group. The data was more variable for females, but this may also merely reflect the outlier. C. The sample mean time was slightly higher for males, but notice the outlier for the male group. The data was more variable for females, but this may also merely reflect the outlier. b. Find the standard error for the difference between the sample means. se = c. Find and interpret a 90% confidence interval comparing the population means. The confidence interval for (μ1 μ 2) is (, ). (Round to the nearest tenth as needed.) Interpret this confidence interval. We are (1) % confident that the difference in the population mean number of hours is between (2) and (3). Since 0 (4) contained in this interval, one (5) females. conclude that the population mean time spent on per week differs for males and 2: Data Table 5 of 8 Males: 0, 0, 1, 1, 2, 2, 3, 4, 5, 5, 9 Females: 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 8, 24

6 (1) 90 (2) -2.7 (3) 2.2 (4) is (5) cannot is not can ID: T 6 of 8

7 1. B. The amount of tax the student is willing to add to a gallon of gasoline. C. Whether the student believes that global warming is a serious issue or not. (1) independent (2) global warming is a serious issue. A. ( x 1 x 2 ) ± t α / 2 (se), B. ( x 2 x 1 ) ± t α / 2 (se) (1) large sample sizes (2) are greater than 0, (3) is greater than A. The samples from the two groups are independent., D. The samples from the two groups are random. 3. B. It does not seem plausible that employment has a normal distribution for each gender because the lowest possible value is 0 and the standard deviations are about the same size as the means, an indication of skew. C. One of the assumptions for this inference is a normal population distribution. The inference is not likely affected because the sample size is very large and the two-sided test is robust with respect to that assumption. A. We can be 95% confident that the population mean gender difference between and hours. μmen μwomen in weekly time spent in employment is No. The population means are not likely equal because 0 does not fall in that range, indicating that there is a difference between genders in the population means with respect to time spent in employment. It appears that men spent more time in employment (on average) than women (1) are less than 0, (2) is less than of

8 5.38 B. The sample mean time was slightly higher for females, but notice the outlier for the female group. The data was more variable for females, but this may also merely reflect the outlier (1) 90 (2) -2.7 (3) 2.2 (4) is (5) cannot 8 of 8