Question 1081224: Compute the p-value in order to test the following hypotheses given that 𝑥̅ = 52, 𝑛 = 9 and 𝜎 = 5.
𝐻0: 𝜇 = 50
𝐻0: 𝜇 > 50
a. Compute the p-value of the test
b. Repeat part a) with 𝑛 = 25
c. Repeat part b) with 𝑛 = 100
d. Discuss what happens to the p-value when the sample size increases.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z-tests
for the first
z=(52-50)/5/sqrt(9)=2*3/5=1.2
p-value is 0.23 with a two way test and 0.115 with a one way test, which is what I think is desired here.
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n=25, sqrt (25) and 2*5/5=2
p=0.0228
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n=100 and 2*10/2, and p-value is 0.00003
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As the sample size increases, the z value increases proportional to the sqrt (n). This means as the size of a sample increases, it is increasingly more difficult for the mean to be further from the postulated true mean.
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