Exam 13: Testing Hypotheses About Means

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 are the appropriate null and alternative hypotheses?

A researcher wants to assess if the time of day during which one works affects job satisfaction. A study compared job satisfaction for day-shift nurses versus night-shift nurses. Independent samples of nurses from each group were obtained and their job satisfaction was measured on a numerical scale with higher scores indicating greater satisfaction. Identify the appropriate parameter for this situation and name an appropriate technique that might be performed provided the underlying assumptions are met.

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. -What is the effect size that should be reported with this 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). -What would be the decision for testing H₀: $\mu$ = 9 versus H_a: $\mu$ $\neq$ 9 at the 10% significance level?

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. -Given an appropriate conclusion using a 5% 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. -What is the p-value for testing whether women score significantly lower on fear 6 months after the course than directly at the end of the course?

The level of significance associated with a significance test is the probability

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. -For a significance level of 0.05, what is the critical value?

An agricultural experiment will be done to compare the effectiveness of two different soil treatments. Which of the following sample sizes would lead to a test with the lowest power?

A random sample of 25 college males was obtained and each was asked to report their actual height and what they wished as their ideal height. A 95% confidence interval for $\mu$ _d = average difference between their ideal and actual heights was 0.8"to 2.2". Based on this interval, which one of the null hypotheses below (versus a two-sided alternative) can be rejected?

In hypothesis testing for one mean, the "null value"is not used in which of the following?

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 value of the test statistic?

Suppose that the average age when women first marry was 23 years in 1960 and 25 years in 1990, with a standard deviation of 2 years in both 1960 and 1990. What is the effect size that measures the increase in age when women get married from 1960 to 1990?

Use the following information for questions: A counselor wants to show that for men who are married by the time they are 30, $\mu$ = average age when the men are married is not 21 years old. A random sample of 10 men who were married by age 30 showed an average age at marriage of 22.2, with a sample standard deviation of 1.9 years. Assume that the age at which this population of men get married for the first time is normally distributed. -For a significance level of $\alpha$ = 0.05, are the results statistically significant?

As Internet usage flourishes, so do questions of security and confidentiality of personal information. A survey of U.S. adults resulted in a 95% confidence interval for the proportion of all U.S. adults who would never give personal information to a company of (0.22, 0.30). Based on this interval, which one of the null hypotheses below (versus a two-sided alternative) can be rejected?

Use the following information for questions: A large car insurance company is conducting a study to see if male and female drivers have the same number of accidents, on average, or if male drivers (who tend to be thought of as more aggressive drivers) have more. Data on the number of accidents in the past 5 years is collected for randomly selected drivers who are insured by this company. An analysis of the results produced the following output. -State the appropriate null and alternative hypotheses and be sure to identify the corresponding parameters.

When comparing two means, the situation most likely to lead to a result that is statistically significant but of little practical importance is

Explain the role of effect size in meta-analyses.

For what problem is a two-sample t-test used?

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