Exam 11: Statistical Inferences Based on Two Samples

The registrar at a state college is interested in determining whether there is a difference of more than one credit hour between male and female students in the average number of credit hours taken during a term. She selected a random sample of 60 male and 60 female students and observed the following sample information. What do you conclude at α = .01? Assume unequal variances.

In which of the following tests is the variable of interest the difference between the values of the observations from the two samples, rather than the actual observations themselves?

Find a 95 percent confidence interval for μ₁ − μ₂, where n₁ = 9, n₂ = 6, ₁ = 64, ₂ = 59, s₁² = 6, and s₂² = 3. (Assume equal population variances.)

Find a 99 percent confidence interval for the difference between means, given that n₁ = 49, n₂ = 49, ₁ = 87, ₂ = 92, s₁² = 13, and s₂² = 15. (Assume unequal variances.)

In testing the difference between the means of two normally distributed populations using independent random samples, the alternative hypothesis always indicates no difference between the two specified means.

When testing the difference between two proportions selected from populations with large independent samples, the z test statistic is used.

In testing the difference between the means of two normally distributed populations using large independent random samples, the sample sizes from the two populations must be equal.

The value of F_α in a particular situation depends on the size of the right-hand tail area and the numerator degrees of freedom.

A marketing research company surveyed grocery shoppers on the East Coast and West Coast to find the percentage of the customers who prefer chicken to other meat. The data are given below. Determine the 95 percent confidence interval for the difference between the proportion of customers on the West Coast who prefer chicken and the proportion of customers on the East Coast who prefer chicken.

A coffee shop franchise owner is looking at two possible locations for a new shop. To help him decide, he looks at the number of pedestrians that go by each of the two locations in one-hour segments. At location A, counts are taken for 35 one-hour units, with a mean number of pedestrians of 421 and a sample standard deviation of 122. At the second location (B), counts are taken for 50 one-hour units, with a mean number of pedestrians of 347 and a sample standard deviation of 85. Assume the two population variances are not known but are equal. Set up the null hypothesis to test the claim that both sites have the same number of pedestrians.

A market research study conducted by a local winery on white wine preference found the following results. Of a sample of 500 men, 120 preferred white wine. Of a sample of 500 women, 210 preferred white wine. Calculate the test statistic for testing the claim that the percentage of women preferring white wine is more than 25 percent higher than that of men.

If the limits of the confidence interval of the difference between the means of two normally distributed populations were from −2.6 to 1.4 at the 95 percent confidence level, then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

A fast-food company uses two management-training methods. Method 1 is a traditional method of training, and Method 2 is a new and innovative method. The company has just hired 31 new management trainees. 15 of the trainees are randomly selected and assigned to the first method, and the remaining 16 trainees are assigned to the second training method. After three months of training, the management trainees take a standardized test. The test was designed to evaluate their performance and learning from training. The sample mean score and sample standard deviation of the two methods are given below. The management wants to determine if the company should implement the new training method. What is the sample value of the test statistic? (Assume equal population variances.)

In testing the difference between two means from two normally distributed independent populations, the distribution of the difference in sample means will be

When testing H₀: μ₁ − μ₂ = 2, H_A: μ₁ − μ₂ > 2, where ₁ = 522, ₂ = 516, s₁² = 28, s₂² = 24, n₁ = 40, n₂ = 30, at α = .01, what can we conclude using critical value rules? (Assume unequal variances.)

Find a 90 percent confidence interval for the difference between the proportions of group 1 and group 2. Let p₁ represent the population proportion of the people in group 1 who like a new mobile app, and let p₂ represent the population proportion of the people in group 2 who like a new mobile app. = .21, = .13, n₁ = 300, and n₂ = 400.

The F statistic can assume either a positive or a negative value.

There are two types of machines, called type A and type B. Both type A and type B can be used to produce a certain product. The production manager wants to compare efficiency of the two machines. He assigns each of the 15 workers to both types of machines to compare their hourly production rate. In other words, each worker operates machine A and machine B for one hour each. These two samples are independent.

What is the value of the computed F statistic for testing equality of population variances where s₁² = .004 and s₂² = .002? Consider H_A: σ₁² > σ₂^2.

In testing the difference between the means of two normally distributed populations using independent random samples, we can only use a two-sided test.