Question

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 approximately Normal. The hypotheses being tested are H0 : 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. It would be unchanged because the variability measured by the standard deviation stays the same.

Answer 1

a) appropriate degrees of freedom for this test =n-1=99

b)

population mean μ=	7.5
sample mean 'x̄=	7.000
sample size   n=	100.00
sample std deviation s=	2.00
std error 'sx=s/√n=	0.2000
test stat t ='(x-μ)*√n/sx=	-2.500
p value      =	0.0141

c)

for 95% CI; and 99 df, value of t=		1.984
margin of error E=t*std error    =		0.397
lower bound=sample mean-E =		6.603
Upper bound=sample mean+E =		7.397
from above 95% confidence interval for population mean =(6.603 , 7.397)

d)

i. It would be larger. (because standard error will increase and therefore test statistic will reduced)