Exam 13: Testing Hypotheses About Means

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: 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. -Are the results statistically significant at the 5% significance level?

Use the following information for questions: For the variable "Time spent watching TV in Typical Day," here are results of a two-sample t-procedure that compares a random sample of men and women at a college. -What is the alternative hypothesis of the t-test?

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. -What is the value of the test statistic?

Use the following information for questions: An airport official wants to assess if the flights from one airline (Airline 1) are less delayed than flights from another airline (Airline 2). 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 9.5 minutes delay with a standard deviation of 3 minutes. A random sample of 10 flights for Airline 2 shows an average of 12.63 minutes delay with a standard deviation of 3 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 is the value of the test statistic?

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 are the appropriate null and alternative hypotheses?

Use the following information for questions: A researcher wants to assess if there is a difference in the average age of onset of a certain disease for men and women who get the disease. Let $µ_1$ = average age of onset for women and $µ_2$ = average age of onset for men. A random sample of 30 women with the disease showed an average age of onset of 83 years, with a sample standard deviation of 11.5 years. A random sample of 20 men with the disease showed an average age of onset of 77 years, with a sample standard deviation of 4.5 years. Assume that ages at onset of this disease are normally distributed for each gender, do not assume the population variances are equal, and use the conservative "by hand" estimate for the degrees of freedom. -For a significance level of $\alpha$ = 0.05, are the results statistically significant?

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 5% 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.

The amount of time the husband and the wife spend on house work is measured for 15 women and their 15 husbands. For the wives the mean was 7 hours/week and for the husbands the mean was 4.5 hours/week. The standard deviation of the differences in time spent on house work was 2.85. What is the value of the test statistic for testing the difference in mean time spent on housework between husbands and wives?

Use the following information for questions: A researcher wants to assess if there is a difference in the average age of onset of a certain disease for men and women who get the disease. Let $µ_1$ = average age of onset for women and $µ_2$ = average age of onset for men. A random sample of 30 women with the disease showed an average age of onset of 83 years, with a sample standard deviation of 11.5 years. A random sample of 20 men with the disease showed an average age of onset of 77 years, with a sample standard deviation of 4.5 years. Assume that ages at onset of this disease are normally distributed for each gender, do not assume the population variances are equal, and use the conservative "by hand" estimate for the degrees of freedom. -What is the value of the test statistic?

Compute the effect size in a test for the difference between two population means with independent samples with sample of sizes of 50 each and a test statistic of t = −2.0.

Use the following information for questions: A sample of n = 9 men are asked. "What's the fastest you've ever driven a car?"The sample mean is 120 mph and the standard deviation is 30. -What is the value of the t-test statistic for testing the null hypothesis that the population mean response is 100 mph?

Which of the following is not one of the steps for hypothesis testing?

Use the following information for questions: Cholesterol measurements for a sample of males following a new diet plan gave a mean of 208 and a standard deviation of 10. -What is the estimated effect size for comparing this result to the 200 level?

Use the following information for questions: A sample of n = 9 men are asked. "What's the fastest you've ever driven a car?"The sample mean is 120 mph and the standard deviation is 30. -What are the degrees of freedom for conducting this t-test?

Use the following information for questions: An airport official wants to assess if the flights from one airline (Airline 1) are less delayed than flights from another airline (Airline 2). 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 9.5 minutes delay with a standard deviation of 3 minutes. A random sample of 10 flights for Airline 2 shows an average of 12.63 minutes delay with a standard deviation of 3 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 $\alpha$ = 0.05, are the results statistically significant?

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. -Which of the following is an appropriate conclusion?

A random sample of 25 third graders scored an average of 3.2 on a standardized reading test. The standard deviation was 0.95. What is the value of the t-test statistic for determining if the mean score is significantly higher than 3?

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