You will perform a significance test of H0 19 based on an S

You will perform a significance test of H0: ?= 19 based on an SRS of n= 25. Assume that ?= 13.

a) If 23, what is the test statistic z? b) What is the P-value if Hs: u> 19? cWhat is the P-value if H 19?

Solution

Answer: z-stat = x-mu/(sigma/n^0.5)

substtute the value in the formula: (23-19)x5 /(13)

=20/13

=1.53.

b) since the z values is 1.53, at a 5% alpha, the z values for the one-sided test is 1.64. Since z stat lies below the z value of 1.6, we know the stat is not significant. This means that the p values must lie below 0.05 at the alpha level of 5%.

c) as the z stat lies in the acceptance region of two-sided test i.e. (-1.96, +1.96), at a 5% significance level, we can accept the stat as it is significant. This means the p values is greater than 0.05