Question #8713

2. A teacher wants to investigate whether there is a difference between male and female students in the amount of time they spend studying for statistics. The table below shows the amount of time students spend studying statistics each week. The amounts of time spent studying are normally distributed.
Male Female
27 25
25 29
19 18
10 23
16 20
17 15
15 19
a. What statistical test should be used to analyze the data?
b. Is this a one- or two tailed test?
c. Identify H0 and Ha for this study.
d. Conduct the appropriate analysis. Should H0 be rejected?

Expert's answer

2. A teacher wants to investigate whether there is a difference between male and female students in the amount of time they spend studying for statistics. The table below shows the amount of time students spend studying statistics each week. The amounts of time spent studying are normally distributed.&

Male Female

27 25

25 29

19 18

10 23

16 20

17 15

15 19

a. What statistical test should be used to analyze the data?

Try an independent groups t-test.

&

b. Is this a one- or two tailed test?

This will be a two-tailed test because the problem is just asking if there is a difference, which could be in either direction.

&

c. Identify H0 and Ha for this study.

Ho: µ1 = µ2 -->population means are equal

Ha: µ1 does not equal µ2 -->population means are not equal

&

d. Conduct the appropriate analysis. Should H0 be rejected?

xbar1 = 18.429

s1 = 5.884

n1 = 7

xbar2 = 21.286

s2 = 4.716

n2 = 7

Pooled variance : Sp^2 = (5.884^2(7 - 1) + 4.716^2(7 - 1))/(7 + 7 - 2) = 28.429

Degree of freedom = 7 + 7 - 2 = 12

Test statistic = (18.429 - 21.286) / sqrt(28.429(1/7 + 1/7)) = -1.002

Let significance level = 0.05

Critical value : t cr = ±2.179

We cannot reject the null hypothesis since the test statistic is not more extreme than the critical values.

We don't have sufficient evidence to conclude that there is a difference between male and female students in the amount of time they spend studying for statistics.

Male Female

27 25

25 29

19 18

10 23

16 20

17 15

15 19

a. What statistical test should be used to analyze the data?

Try an independent groups t-test.

&

b. Is this a one- or two tailed test?

This will be a two-tailed test because the problem is just asking if there is a difference, which could be in either direction.

&

c. Identify H0 and Ha for this study.

Ho: µ1 = µ2 -->population means are equal

Ha: µ1 does not equal µ2 -->population means are not equal

&

d. Conduct the appropriate analysis. Should H0 be rejected?

xbar1 = 18.429

s1 = 5.884

n1 = 7

xbar2 = 21.286

s2 = 4.716

n2 = 7

Pooled variance : Sp^2 = (5.884^2(7 - 1) + 4.716^2(7 - 1))/(7 + 7 - 2) = 28.429

Degree of freedom = 7 + 7 - 2 = 12

Test statistic = (18.429 - 21.286) / sqrt(28.429(1/7 + 1/7)) = -1.002

Let significance level = 0.05

Critical value : t cr = ±2.179

We cannot reject the null hypothesis since the test statistic is not more extreme than the critical values.

We don't have sufficient evidence to conclude that there is a difference between male and female students in the amount of time they spend studying for statistics.

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