Question

if you collect a sample of size 13 with a sample mean of 54 and a standard error of the mean of 6, REPORT THE P-VALUE if the test the hypothesis that the true mean is equal to 55 using a two tailed test

Answer 1

Let be the true mean.

the hypotheses are

The sample information is

n=13 is the sample size

is the sample mean

is the standard error of the mean

is the hypothesized value of mean (from the null hypothesis)

Since the sample size is less than 30 and we do not know the population standard deviation, we will use t- distribution for the sample statistics.

This is a 2 tailed test (the alternative hypothesis has "not equal to")

The p-value if

the degrees of freedom is n-1=13-1=12

Using excel function =T.DIST.2T(0.167,12), we get a p-value=0.8702

We will reject the null hypothesis if the p-value is less than the significance level.

For example for a significance level alpha=0.05, we can see that the p-value of 0.8702 is greater than alpha=0.05.

Hence we do not reject the null hypothesis.

We conclude that there is no evidence against the claim that the true mean is equal to 55