Question

One of the many concerns of college students today is the time required for them to graduate with a baccalaureate degree (BA or BS). Current estimates in the California public university system is that takes an average of slightly over 5 years for a student to complete a baccalaureate degree. One researcher suggests that males take a significantly longer average time than females to complete a baccalaureate degree. In this situation, suppose that two independent random samples from approximately normal distributions were taken from recent college graduates of the California public university system. As before, we let u2 represent the average time it takes males to complete a baccalaureate degree in the California public university system.

Using the summary data below from the two samples, compute the value of the test statistic t^*.
x1=4.95 x2=5.22
s1=0.64 s2=0.89
n1=21 n2=21
Choose one answer.
(A) -1.78
(B) -1.59
(C) -1.13
(D) -1.00
(E) -0.84

Answer 1

The correct option is C.

Explanation:

Given information:

`\overline{x}_1=4.95`

`\overline{x}_2=5.22`

`s_1=0.64`

`s_2=0.89`

`n_1=n_2=21`

The formula for t test statistic t* is

`t^*=\frac{(\overline{x}_1-\overline{x}_2)-(\mu_1-\mu_2)}{\sqrt{(s_1^2)/(n_1)+(s_2^2)/(n_2)}}`

Using the formula we get

`t^*=\frac{\left(4.95-5.22\right)-(0)}{\sqrt{(0.64^2)/(21)+(0.89^2)/(21)}}`

`t^*=-1.12869182873`

`t^*\approx -1.13`

The value of test statistic t* is -1.13. Therefore the correct option is C.