Question

1. A university was studied last fall to see if male students studied for a different amount of time than females during the week. The following data was collected and now, we need to be able to perform analysis on this data in order to help this university understand their student population and what changes they may be able to put into effect.

Group	n	Mean	StDev
Females	1117	2.99	2.34
Males	870	2.86	2.22

a) Perform an appropriate significance test and interpret it.

Answer 1

n1 = 1117

= 2.99

s1 = 2.34

= 5.4756

n2 = 870

= 2.86

s2 = 2.22

= 4.9284

Claim:male students studied for a different amount of time than females during the week.

The null and alternative hypothesis is

For doing this test first we have to check the two groups have population variances are equal or not.

The null and alternative hypothesis is

Test statistic is

F = largest sample variance / Smallest sample variances

F = 5.4756 / 4.9284 = 1.11

Degrees of freedom => n1 - 1 , n2 - 1 => 1117 - 1 , 870 - 1 => 1116 , 869

Critical value = 1.12

Critical value > test statistic so we fail to rejthe ect null hypothesis.

Conclusion: The population variances are equal.

So we have to use here pooled variance.

Test statistic is

Degrees of freedom = n1 + n2 - 2 = 1117 + 870 - 2 = 1985

Critical value = 1.96

| t | < critical value we fail to reject null hypothesis.

Conclusion: male students studied NOT the different amount of time than females during the week.