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A sample of 38 observations is selected from a normal population. The sample mean is 47,...

  1. A sample of 38 observations is selected from a normal population. The sample mean is 47, and the population standard deviation is 7. Conduct the following test of hypothesis using the 0.05 significance level. H0: μ = 48; H1: μ ≠ 48      (20 pts)
    1. Is this a one- or two-tailed test
    1. What is the decision rule?
    1. What is the value of the test statistic?
    1. What is your decision regarding H0?
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Answer #1

a)

Rejection Region
This is two tailed test, for α = 0.05


b)

Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96


c)


Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (47 - 48)/(7/sqrt(38))
z = -0.88

d)


Rejection Region Approach
As the value of test statistic, z is within critical value range, fail to reject the null hypothesis

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