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A simple random sample of 101 postal employees is used to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years recorded 20 years ago. The sample mean was x¯ = 7 years with a standard deviation of s = 2 years. Assume the distribution of the time the employees have worked for the postal service is approximately Normal. The hypotheses being tested are H0: μ= 7.5, Ha: ≠ 7.5. A one-sample t test will be used.
What is a 95% confidence interval for μ, the population mean time the postal service employees have spent with the postal service?
Suppose the mean and standard deviation obtained were based on a sample of size n = 25 postal workers rather than 101. What do we know about the value of the P-value?
A) It would be smaller.
B) It would be larger.
C) It would be unchanged, because the difference between and the hypothesized value = 7.5 is unchanged.
D) It would be unchanged, because the variability measured by the standard deviation stays the same.
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