A simple random sample of 100 postal employees is used to test if the average ti

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 7 years with a standard deviation of 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:   = 7.5, HA:   7.5. A one-sample t test will be used.

What are the appropriate degrees of freedom for this test?

a- 7

b- 19     

c- 99

d- 100

What is the value of the test statistic for the one-sample t?

a- 2

b- -0.25     

c- 2.5

d- -2.5

What is the p-value for the one-sample t?

a- 0.0062

b- 0.02 > p-value > 0.01     

c- 0.01 > p-value > 0.005

d- 0.10 > p-value > 0.05

e- 0.05 > p-value > 0.01

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?

a- It would be smaller.

b- It would be larger.     

c- It would be unchanged because the difference between the sample mean and the hypothesized mean is the same.

d- It would be unchanged because the variability or standard deviation is the same.

What would you conclude about the population?

a- The true average years is equal to 7.5

b- The true average years is not equal to 7.5     

c- The true average years is greater than 7.5

d- Not enough information

Explanation / Answer

The statistical software output for this problem is:

One sample T hypothesis test:
: Mean of population
H0 : = 7.5
HA : 7.5

Hypothesis test results:

So,

Degrees of freedom = 99; Option C

Test statistic = -2.5; Option D

p - value = 0.0141; So 0.02 > p - value > 0.01; Option B

In case of n = 25, p - value would be larger. Option B

Since level of significance is not given, we do not have enough information to make conclusion. Option D

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