A simple random sample of 100 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 approximatelyNormal. The hypotheses being tested areH0 : μ = 7.5,Ha : μ , 7.5. A one-sample t test will be used. (a) What are the appropriate degrees of freedom for this test? (b) What is the P-value for the one-sample t test? (c) What is a 95% confidence interval for m, the population mean time the postal service employees have s
A simple random sample of 100 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 approximatelyNormal. The hypotheses being tested areH0 : μ = 7.5,Ha : μ , 7.5.
A one-sample t test will be used.
(a) What are the appropriate degrees of freedom for this test?
(b) What is the P-value for the one-sample t test?
(c) What is a 95% confidence interval for m, the population mean time the postal service
employees have spent with the postal service?
(d) Suppose the mean and standard deviation obtained were based on a sample of size
n = 25 postal workers rather than 100. What do we know about the value of the
P-value?
i. It would be larger.
ii. It would be smaller.
iii. It would be unchanged because the difference between and the hypothesized
value m = 7.5 is unchanged.
iv. Itwould be unchanged because the variabilitymeasured by the standard deviation
stays the same.
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