SOLUTION: A sample of 40 sales receipts from a grocery store has x= 137 and s=30.Use these values to test whether or not the mean is sales at the grocery store are different from 150.

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Question 1203211: A sample of 40 sales receipts from a grocery store has x= 137 and s=30.Use these values to test whether or not the mean is sales at the grocery store are different from 150.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
sample size = 40
sample standard deviation = 30
sample mean = 137
test mean = 150
standard error of test is standard deviation / square root of sample size = 30 / sqrt(40) = 4.7434.
since sample standard deviation is used, rather than population standard deviation, use of t-score is indicated.
t = (x - m) / s
t is the t-score
x is the sample mean
m is the test mean
s is the standard error.
formula becomes t = (137 - 150) / 4.7434 = -2.74065.
area to the left of that t-score with 39 degrees of freedom = .00436017756.
that's your test alpha.
two tailed critical alpha on the low side of the confidence is typically as low as .005.
test alpha is less than that, so results are significant, indicating the sales at the grocery store are diffeenct from the test sales mean of 150.
note that .005 critical alpha is very restrictive.
it is normally .025 (that's .95 confidence interval with two tailes totaling .05, with .025 on each end.

Answer by ikleyn(52790) (Show Source):
You can put this solution on YOUR website!
.
A sample of 40 sales receipts from a grocery store has x= 137 and s=30. Use these values
to test whether or not the mean is sales at the grocery store are different from 150.
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As presented in the post, the problem is posed/worded INCORRECTLY.

To be correct, the problem must include the "confidence interval" value,
which is missed in the post.