SOLUTION: In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. The bookstore believes that the two groups spent the

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Question 1201206: In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. The bookstore believes that the two groups spent the same amount. What is an appropriate test value for a z test?
Sample size: freshmen 50, seniors 60
Sample mean freshmen $480, seniors $500
Population std.dev. freshmen $52, seniors $63

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
since you know the population standard deviation, i believe you can use the z-score.
note that the sample size is greater than 30 as well.

here's a refernce on when to use t-score versus when to use z-score.
https://math.stackexchange.com/questions/1817980/how-to-know-when-to-use-t-value-or-z-value

freshmen:
sample size is 50
sample mean is 480
population standard deviation is 52

seniors:
sample size is 60
sample mean is 500
population standard deviation is 63

standard error of the test is sqrt(52^2/50 + 63^2/60) = 10.964974414.

mean difference is 20
standard error is 10.964974414
z-score is 20 / that = 1.8239947

critical z-score for 95% two tailed confidence interval is equal to plus or minus 1.96
since test z-score is within these limits, the results are not significant and the conclusion is that the means of the two samples are not considered to be different.
if you want to use p-value, then:
the two-tailed p-value is .034 * 2 (.034 on the left and .034 on the right) which is equal to .068 which is greater than two tailed critical p-value of .05.
note that the two tailed critical p-value is divided by 2 to get a p-value of .025 on each end.
here are the results from the calculator i found at https://www.statskingdom.com/120MeanNormal2.html that confirms these results.