Cconsider the following null and alternative hypotheses: Ho: u 5.5 vs. Ha: u <5.
ID: 3384042 • Letter: C
Question
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
Explanation / Answer
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
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