Question 1203211
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.