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

a. -2.5

b. 2.5    

c. -0.25

d. 2

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

a. 0.02 > p-value > 0.01

b. 0.10 > p-value > 0.05

c. 0.01 > p-value > 0.005

d. 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 unchanged because the variability or standard deviation is the same.    

c. It would be larger.

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

What would you conclude about the population?

a. The true average years is not equal to 7.5

b. The true average years is greater than 7.5    

c. The true average years is equal to 7.5

d. Not enough information

Explanation / Answer

H0 : mu = 7.5 vs H1 : mu < 7.5

n = 100 ,

test statistic = [xbar-mu]/[sd/sqrt(n)] = [7 - 7.5 ] / [2/sqrt(100) ] = -2.5

The P-Value is 0.00621.

2)The result is significant at p < 0.05.

3) c. It would be larger.

4) a. The true average years is not equal to 7.5

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.