Exam 13: Testing Hypotheses About Means

Use the following information for questions: A group of women suffering from various types of obsessive fear is given a therapeutic course to learn how to handle their fear. At the end of the course the women are given a questionnaire to determine how afraid they are. Six months after the course the women answer the questionnaire again as a follow-up measure. The fear-scores are typed into SPSS. Output of the paired samples t-test is shown below. -Based on Cohen's interpretation, this effect is

Use the following information for questions: An instructor wanted to prove that writing with the non-dominant hand takes longer on average than writing with the dominant hand. A significance level of 5% will be used. Ten students randomly sampled from a large class each wrote the word "Statistics" twice; once with their dominant hand and once with their non-dominant hand, in random order. The average time to write using their dominant hands was 5 seconds, while the average time to write with their non-dominant hand was 10 seconds. The standard deviation of the difference was 7.9 seconds, and the standard error was 2.498. Assume that writing times with each hand are normally distributed. -What are the degrees of freedom for conducting this t-test?

Use the following information for questions: Unoccupied seats on flights cause airlines to lose revenue. A large airline wanted to estimate its average number of unoccupied seats per flight. Based on a random sample of flights, the 95% confidence interval for mean number of unoccupied seats per flight was given as: (7.5, 9.5). -Based on the 95% confidence interval, what would be the decision for testing H₀: $\mu$ = 7 versus H_a: $\mu$ $\neq$ 7 at the 5% significance level?

Use the following information for questions: Conscientiousness is a tendency to show self-discipline, act dutifully, and aim for achievement. The trait shows a preference for planned rather than spontaneous behavior. A random sample of 650 students is asked to fill out the Hogan Personality Inventory (HPI) to measure their level of conscientiousness. The 300 undergraduate students scored an average of 148 with a standard deviation of 16. The 350 graduate students had a mean score of 153 with a standard deviation of 21. Is this enough evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students? -What are the appropriate null and alternative hypotheses?

Use the following information for questions: In the survey of a random sample of students at a university, two questions were "How many hours per week do you usually study?" and "Have you smoked marijuana in the past six months?" An analysis of the results produced the following Minitab output: -Which of the following is the appropriate unpooled test statistic for determining if there is a difference in average study hours per week for the two groups?

One hundred adults who had either Type 1 or Type 2 diabetes were divided into 2 groups to determine if the inhalable version of insulin is able to manage blood sugar levels just as well as injected insulin. At the end of the trial period we count the number of Type 1 diabetics who reacted better to the inhaler than to the injections. We do the same for the Type 2 diabetics. If we wish to determine if there is a difference in the percentages of diabetics who reacted better to the inhaler between Type 1 and Type 2 diabetics, which inference procedure should we use?

Use the following information for questions: Spatial perception is measured on a scale from 0 to 10. Two groups of 8^th grade children are tested for spatial perception. The students in group 1 were first given a short course on spatial concepts. The students in group 2 received no such instruction. SPSS was used to calculate descriptive statistics for the two samples. -Which of the following is an appropriate conclusion?

Use the following information for questions: A safety officer wants to prove that $\mu$ = the average speed of cars driven by a school is less than 25 mph. Suppose that a random sample of 14 cars shows an average speed of 24.0 mph, with a sample standard deviation of 2.2 mph. Assume that the speeds of cars are normally distributed. -What is the value of the test statistic?

Using Cohen's interpretation of effect size, what would an effect size of d = −0.52 be interpreted as?

Which of the following is not a correct way to state a null hypothesis?

One hundred adults who had either Type 1 or Type 2 diabetes were divided into 2 groups to determine if the inhalable version of insulin is able to manage blood sugar levels just as well as injected insulin. The first group received the inhaler; the second group continued using their injections. If we wish to determine if there is a difference in average blood sugar levels at the end of the trial period between the inhaler group and the injection group, which inference procedure should we use?

Use the following information for questions: Unoccupied seats on flights cause airlines to lose revenue. A large airline wanted to estimate its average number of unoccupied seats per flight. Based on a random sample of flights, the 95% confidence interval for mean number of unoccupied seats per flight was given as: (7.5, 9.5). -What was the mean number of unoccupied seats per flight for the sample of flights?

In each of the following cases, we wish to test the null hypothesis H₀: $\mu$ =10 vs. H_a: $\mu$ $\neq$ 10. In which case can this null hypothesis not be rejected at a significance level $\alpha$ = 0.05?

Use the following information for questions: A researcher wants to assess if the average age when women first marry has increased from 1960 to 1990. Let $µ_1$ = average age of first marriage for women in 1990 and $µ_2$ = average age of first marriage for women in 1960. A random sample of 10 women married in 1990 showed an average age at marriage of 24.95 years, with a sample standard deviation of 2 years. A random sample of 20 women married in 1960 showed an average age at marriage of 23.1 years, with a sample standard deviation of 1.5 years. Assume that age of first marriage for women is normally distributed, but do not assume the population variances are equal. Use the conservative "by hand" estimate for the degrees of freedom. -What is the p-value?

Use the following information for questions: A group of women suffering from various types of obsessive fear is given a therapeutic course to learn how to handle their fear. At the end of the course the women are given a questionnaire to determine how afraid they are. Six months after the course the women answer the questionnaire again as a follow-up measure. The fear-scores are typed into SPSS. Output is shown below. -What is the value of the standard deviation of the differences that is missing from the output?

At entrance C of the football stadium there are 3 swing gates for the spectators. On football Saturday, two high school students sit at this entrance and count the number of people who enter through each of the swing gates. They also write down the gender of these spectators. On Monday, during their statistics class, they wish to determine if men are more likely to enter through the middle swing gate than women. What is the appropriate parameter in this situation?

Use the following information for questions: An investigator wants to assess whether the mean $\mu$ = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 51 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed. -Which of the following is an appropriate conclusion?

Compute the effect size in a one-sample t-test with a sample size of n = 66 and a test statistic of t = 2.27. How is the effect size interpreted based on Cohen's guidelines?

Use the following information for questions: A small bakery is trying to predict how many loaves of bread to bake daily. They randomly sample daily sales records from the past year. In these days, the bakery sold between 40 and 80 loaves per day with a 95% confidence interval for the population mean daily loaf demand given by (51, 54). -Based on this interval, what is the decision for testing H₀: $\mu$ = 52 versus H_a: $\mu$$\neq$ 52 at the 10% significance level?

Use the following information for questions: An investigator wants to assess whether the mean $\mu$ = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 51 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed. -What is the p-value?