SOLUTION: To conduct a hypothesis test of the claim that the population mean satisfaction rating of ABC employees is different from 3.2, you choose a random sample of 13 surveys. The sample

Question 1203193: To conduct a hypothesis test of the claim that the population mean satisfaction rating of ABC employees is different from 3.2, you choose a random sample of 13 surveys. The sample has a mean satisfaction rating of 3.3 and a standard deviation of 0.6. If the sample is from a normally distributed population with an unknown standard deviation, choose an appropriate test statistic for your hypothesis test on the population mean. Then calculate that statistic. Round to two decimal.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you would use the t-test because the standaard deviation is taken from the sample rather than from the population.
n = sample size = 13
pm = population mean = 3.2
sm = sample mean = 3.1
ssd = sample standard deviation = .6
sdof = sample degrees of freedom = sample size minus 1 = 12
se = standard error = ssd / sqrt(n) = sample standard deviation / square root of sample size = .6/sqrt(13) = .1664
t = (x - m) / s is your formula.
t = t-score
x = sample mean
m = population mean
s = standad error
formula becomes t = (3.1 - 3.2) / .1664 = -.60096
you would get the area to the left of that t-score with 12 degrees of freedom.
that's the test alpha which is equal to test p-value which is equal to .2795.
round to two decimal places to get .28.
that is compared to the critical p-value, which is usually .05 or .025 or .01.
the test results are considered significant if the test p-value is less than the critical p-value.
another test value would be the test t-score compare to the critical t-score.
your test t-score is equal to -.60096.
the critical t-score on the left side of the normal distribiution with 12 degrees of freedom is usually -1.78 at .05 critical alpha, or -2.18 at .025 critical slpha, or -2.68 at .01 critical alpha.
the test results are considered significant if the test t-score is greater than the critical t-score.
the two measures support each othr.
if the test t-score is greater than the critical t-score, then the test alpha is less than the critical alpha, and vice versa.
your test t-store is less than the critical t-score and your test alpha is greater than your critical alpha, both indications that the results are not significant.

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