Cconsider the following null and alternative hypotheses Ho u

Cconsider the following null and alternative hypotheses: Ho: u     5.5 vs. Ha: u <5.5.

Given a significance level of 0.01 and a random sample of size 5 with a sample mean of 5.07 and a sample standard deviation of 0.16, determine the following.

A) the critical value(s) for the hypothesis test. Please include a graphical sketch with the critical value(s):

B) calculate the numerical value of the appropriate test statistic for this test:

C) Would you reject or fail to reject Ho? Explain reasoning

Solution

n =5

alpha = 0.01

SD = 0.16

Mean = 5.07

dF= 5-1 =4

A) Critical value = 3.75

B)

t = ( X - mu )/(SD/sqrt(n))

= ( 5.07 - 5.5)/(0.16/sqrt(5))

= -6.0

C)

The P-Value = 0.001941.

Since , P-value < 0.01

Failed to reject null hypothesis H0