Question

Do female college students spend more time than male college students watching TV? 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 three-week period.

For the sample of males, the mean time spent watching TV per day was 68.8 minutes and the standard deviation was 67.5 minutes. For the sample of females, the mean time spent watching TV per day was 93.8 minutes and the standard deviation was 89.1 minutes. Is there convincing evidence that the mean time female students at this university spend watching TV is greater than the mean time for male students? Test the appropriate hypotheses using

α = 0.05.

(Use a statistical computer package to calculate the P-value. Use μ_males − μ_females. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t	=
df	=
P-value	=

State your conclusion.

a.Reject H₀. We do not have convincing evidence that the mean time female students at this university spend watching TV is greater than the mean time for male students.

b.Fail to reject H₀. We have convincing evidence that the mean time female students at this university spend watching TV is greater than the mean time for male students.     

c.Reject H₀. We have convincing evidence that the mean time female students at this university spend watching TV is greater than the mean time for male students.

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

Answer 1

Given that,

For Male : n1 = 46, x1-bar = 68.8 minutes and s1 = 67.5 minutes

For Female : n2= 38, x2-bar =93.8 minutes and s2 = 89.1 minutes

The null and alternative hypotheses are,

H0 : μmales - μfemales = 0

Ha : μmales - μfemales < 0

Using TI-83 plus calculator we get,

Test statistic = t = -1.42

Degrees of freedom = df = 68

p-value = 0.079

Since, p-value is greater than α = 0.05, we fail to reject the null hypothesis.

Conclusion : Fail to reject H0. We do not have convincing evidence that the mean time female students at this university spend watching TV is greater than the mean time for male students.

Answer : d)