Question

The average college student commutes 6.3 miles to school, with a known standard deviation of five miles. John believes that social science majors are different from the average college student. He gets a sample of six social science majors and asks them how far they commute. They answer 4, 13, 11, 7, 15, 10. Do a z-test to see if John’s belief is true. Please calculate the z-statistic for this data.
Now, for the above question, state the critical value, and come to a conclusion about John's belief. Let α = .01. Make it a two-tailed test.

Answer 1

	x
	4
	13
	11
	7
	15
	10
Total	60

n=6

Sample mean

Also we have the known standard deviation

We have to test

H₀:

H₁:

The test statistic to test the above hypotheses is

The value of test statistic for above test is 1.8126

Here we have α=0.01 and we have two tailed test, so for critical value we need table value of z at 0.005 level of significance.

i.e. critical value = z_0.005= 2.575829

Here we can see that the calculated z statistic is less than the critical value of z and it suggests that we do not have enough evidence against null hypothesis to reject it, so we fail to reject the null hypothesis and conclude that John’s belief that social science majors are different from the average college student is not true.