if the null hypothesis is that the mean is 3218, the alternative hypothesis is that the mean > 3228, and the sample mean is x= 3342, the sample standard deviation is s=287, the sample size is n= 42, and α= 0.01

Question

if the null hypothesis is that the mean is 3218, the alternative hypothesis is that the mean > 3228, and the sample mean is x= 3342, the sample standard deviation is s=287, the sample size is n= 42, and α= 0.01

a. calculate the z test statistic.

b. what is the p-value?

c. would this null hypothesis be rejected or not? justify answer with the p-value.

Answer 1

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.