Exam 13: Testing Hypotheses About Means

An experiment will be conducted to compare the effectiveness of a new treatment against a placebo. Which of the following combinations would lead to a test with the highest power?

Which of the following is not true about hypothesis testing?

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? -Which of the following is an appropriate conclusion?

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 used the inhaler for 3 months first and then the injections for 3 months. The other group used the two methods in reverse order. If we wish to determine if there is a difference in average blood sugar levels using the two different methods, which inference procedure should we use?

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 beginning of the course the women are given a questionnaire to determine how afraid they are. Fear scores range between 100 and 400. SPSS is used to obtain descriptive statistics. Output is shown below. The course coordinator wishes to test if the women score significantly lower than 250. -Give an appropriate conclusion using a 10% level of significance.

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. -How much lower, on average, did the women score on the fear questionnaire six months after the course than directly at the end of the course?

Compute the effect size in a one-sample t-test with a sample size of n = 25 and a test statistic of t = 2.00.

The p-value for a one-sided test for a mean was 0.04. The p-value for the corresponding two-sided test would be:

Using Cohen's interpretation of effect size, what would an effect size of d = 0.12 be interpreted as?

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: $\mu$ = 9 versus H_a: $\mu$ $\neq$ 9 at the 5% significance level?

A study compared the average number of courses taken by a random sample of freshmen at a university with the average number of courses taken by a separate random sample of freshmen at a community college. Which of the following combinations would lead to a test with the highest power?

Use the following information for questions: A researcher wants to assess if there is a difference in the average life spans between men and women in Japan. Let $µ_1$ = average life span of Japanese women and $µ_2$ = average life span of Japanese men. A random sample of 10 women showed an average lifespan of 83 years, with a sample standard deviation of 7 years. A random sample of 10 men showed an average lifespan of 77 years, with a sample standard deviation of 6.4 years. Assume that life spans are normally distributed and that the population variances are equal. -What is the p-value?

A null hypothesis is that the mean cholesterol level is 200 in a certain age group. The alternative is that the mean is not 200. Which of the following is the most significant evidence against the null and in favor of the alternative?

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. -For a significance level of $\alpha$ = 0.05, are the results statistically significant?

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. -Find the p-value for testing whether using the non-dominant hand takes longer on average than using the dominant hand?

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 would be the decision for testing H₀: $\mu$ = 7 versus H_a: $\mu$ $\neq$ 7 at the 10% significance level?

Using Cohen's interpretation of effect size, what would an effect size of d = 0.83 be interpreted as?

The headline of a newspaper reads: "More college students than expected use tobacco." The article went on to say that a recent survey shows a significant increase in the use of tobacco among college students with about one-third of college students reporting having used tobacco in the past 30 days. Comment on what a person should consider in evaluating the quality of this reported study result.

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 is the value of the pooled sample variance for the difference between the two sample means?

Use the following information for questions: A bank official wants to assess if the average delays for two airlines are different.Let $µ_1$ = average delay for Airline 1 and $µ_2$ = average delay for Airline 2. A random sample of 10 flights for Airline 1 shows an average of 6 minutes delay with a standard deviation of 5 minutes. A random sample of 10 flights for Airline 2 shows an average of 12 minutes delay with a standard deviation of 5 minutes. Assume delay times are normally distributed, but do not assume the population variances are equal. Use the conservative "by hand" estimate for the degrees of freedom. -What are the appropriate null and alternative hypotheses?