Question

Sprint would like to investigate if women average more minutes per month talking on their cell phones than men. The following data show the number of minutes per month that a random sample of men and women talked on their cellular telephones, analyzed at alpha = 0.05. Test if the average number of minutes used by women exceeds the average number of minutes used by men.

t-Test: Two-Sample Assuming Unequal Variances

Women

Men

Mean	Women 461.1	Men 330.7
Variance	25,993.7	8,247.3
Observations	10	10
Hypothesized Mean Difference	0
Df	14
t Stat	2.228
P(T<=t) one-tail	0.021
t Critical one-tail	1.761
P(T<=t) two-tail	0.043
t Critical two-tail	2.145

What is the conclusion of the test at the 0.05 significance level concerning the women’s and men’s use of cell phone minutes?

a) Conclude that there is evidence to suggest that the women’s use of cell phone minutes exceeds that of men, on average.

b) Conclude that there is insufficient evidence to support the claim that average minutes is different for men and women.False

c) Conclude that there is insufficient evidence to support the claim that women’s average cell phone minute use is greater than men’s average cell phone minute use.

If the level of significance was 0.01, what is the conclusion?

a) Conclude that there is insufficient evidence to support the claim that women’s average cell phone minute use is greater than men’s average cell phone minute use.

b) Conclude that there is evidence to support the claim that women use more cell phone minutes on average .

c) Conclude that there is insufficient evidence to support the claim that average minutes is different for men and women.

Answer 1

Solution:

Given that, Sprint would like to investigate if women average more minutes per month talking on their cell phones than men. The analysis of the result is given and we have to test the hypothesis.

The hypothesis to be stated as:

Ho: The average number of minutes used by women do not exceeds the average number of minutes used by men.

H1: The average number of minutes used by women exceeds the average number of minutes used by men.

This is a one - tail test

1) What is the conclusion of the test at the 0.05 significance level concerning the women’s and men’s use of cell phone minutes?

Since P - value is 0.021, which is less than 0.05, so we reject the Ho at 5% level of significance. Hence, Option a is correct. i.e.

a) Conclude that there is evidence to suggest that the women’s use of cell phone minutes exceeds that of men, on average.

2) If the level of significance was 0.01, what is the conclusion?

Since p-value is 0.021, which is greater than 0.01, so we do not reject the Ho at 1 % level of significane. Hence, option (a) is correct.

a) Conclude that there is insufficient evidence to support the claim that women’s average cell phone minute use is greater than men’s average cell phone minute