Question

An article in American Demographics investigated consumer habits at the mall. We tend to spend the most money shopping on the weekends, and, in particular, on Sundays from 4 to 6 p.m. Wednesday morning shoppers spend the least! Suppose that a random sample of 21 weekend shoppers and a random sample of 21 weekday shoppers were selected, and the amount spent per trip to the mall was recorded.

	Weekends	Weekdays
Sample Size	21	21
Sample Mean ($)	75	62
Sample Standard Deviation ($)	28	21

(a)

Is it reasonable to assume that the two population variances are equal? Use the F-test to test this hypothesis with

α = 0.05.

State the null and alternative hypotheses.

H₀: σ₁² < σ₂² versus H_a: σ₁² > σ₂²H₀: σ₁² = σ₂² versus H_a: σ₁² > σ₂²    H₀: σ₁² = σ₂² versus H_a: σ₁² ≠ σ₂²H₀: σ₁² ≠ σ₂² versus H_a: σ₁² = σ₂²H₀: σ₁² = σ₂² versus H_a: σ₁² < σ₂²

State the test statistic. (Round your answer to two decimal places.)

F =

State the rejection region. (Round your answer to two decimal places.)

F >

State the conclusion.

H₀ is not rejected. There is insufficient evidence to indicate a difference between the two population variances.H₀ is not rejected. There is sufficient evidence to indicate a difference between the two population variances.    H₀ is rejected. There is insufficient evidence to indicate a difference between the two population variances.H₀ is rejected. There is sufficient evidence to indicate a difference between the two population variances.

(b)

Regardless of the answer you found in part (a), assume that the two population variances are equal. Use the appropriate test to determine whether there is a difference in the average amount spent per trip on weekends versus weekdays. Use

α = 0.05.

(Use μ₁ for weekends and μ₂ for weekdays.)

State the null and alternative hypotheses.

H₀: (μ₁ − μ₂) = 0 versus H_a: (μ₁ − μ₂) > 0H₀: (μ₁ − μ₂) = 0 versus H_a: (μ₁ − μ₂) ≠ 0    H₀: (μ₁ − μ₂) < 0 versus H_a: (μ₁ − μ₂) > 0H₀: (μ₁ − μ₂) ≠ 0 versus H_a: (μ₁ − μ₂) = 0H₀: (μ₁ − μ₂) = 0 versus H_a: (μ₁ − μ₂) < 0

State the test statistic. (Round your answer to three decimal places.)

t =

State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

t>t<

State the conclusion.

H₀ is rejected. There is sufficient evidence to conclude that there is a difference in the average amount spent per trip on weekends versus weekdays.H₀ is not rejected. There is sufficient evidence to conclude that there is a difference in the average amount spent per trip on weekends versus weekdays.    H₀ is rejected. There is insufficient evidence to conclude that there is a difference in the average amount spent per trip on weekends versus weekdays.H₀ is not rejected. There is insufficient evidence to conclude that there is a difference in the average amount spent per trip on weekends versus weekdays.

Answer 1