Someone claims that firstyear students in New Jersey public

Someone claims that first-year students in New Jersey public universities are as tall on average as first-year students in Pennsylvania public universities. To test that claim, you collect samples of 100 students from each of the two states and obtain the following results: The mean height for New Jersey students is 65 inches and the mean height for Pennsylvania students is 64 inches. Assume that population standard deviations are known and are 8 inches for both New Jersey and Pennsylvania. Using a significance level of 0.05, what is/are the critical value(s)?

There are two critical values. They are -2.58 and +2.58.

There is only one critical value. It is +2.58.

There is only one critical value. It is +1.96.

There are two critical values. They are -1.96 and +1.96.

Continuing with the example about first-year university students from the previous question, what is the sample value of the test statistic?

14.3019 (or -14.3019 dependent on how you set up the test statistic)

0.8839 (or -0.8839 dependent on how you set up the test statistic)

1.2357 (or -1.2357 dependent on how you set up the test statistic)

1.64 (or -1.64 dependent on how you set up the test statistic)

Solution

There are two critical values. They are -1.96 and +1.96

To find sample value:

Mean diff = 65-64 = 1

std dev equal = 8

std error = 8/rt 100 =0.8

Sample value = 1/std error

= 1.25

1.2357 (or -1.2357 dependent on how you set up the test statistic) is right answer.