Question

Do male college students spend more time studying than female college students? This was one of the questions investigated by the authors of an article. Each student in a random sample of 46 male students at a university in England and each student in a random sample of 38 female students from the same university kept a diary of how he or she spent time over a 3-week period.

For the sample of males, the mean time spent studying per day was 283.0 minutes and the standard deviation was 160.4 minutes. For the sample of females, the mean time spent studying was 183.8 minutes and the standard deviation was 166.4 minutes. Is there convincing evidence that the mean time male students at this university spend studying is greater than the mean time for female students? Test the appropriate hypotheses using

α = 0.05.

(Use μ₁ for male students and μ₂ for female students.)

State the appropriate null and alternative hypotheses.

H₀: μ₁ − μ₂ > 0 and H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ = 0 and H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ < 0 and H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ = 0 and H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ > 0 and H_a: μ₁ − μ₂ = 0

Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.)

t=

P-value=

State the conclusion in the problem context.

We reject H₀. We have convincing evidence that the mean time male students at this university spend studying is greater than the mean time for female students.

We fail to reject H₀. We have convincing evidence that the mean time male students at this university spend studying is greater than the mean time for female students.    

We fail to reject H₀. We do not have convincing evidence that the mean time male students at this university spend studying is greater than the mean time for female students.

We reject H₀. We do not have convincing evidence that the mean time male students at this university spend studying is greater than the mean time for female students.

Answer 1