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: μ = 7.5, H_A: μ ≠ 7.5. A one-sample t test will be used.

What are the appropriate degrees of freedom for this test?

19? 7? 99? 100?

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

2? 2.5? -2.5? -0.25?

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

0.0062? 0.05 > p-value > 0.01 ? 0.02 > p-value > 0.01? 0.10 > p-value > 0.05? 0.01 > p-value > 0.005

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?

It would be unchanged because the difference between the sample mean and the hypothesized mean is the same.? It would be larger. ? It would be smaller.? It would be unchanged because the variability or standard deviation is the same.?

What would you conclude about the population?

The true average years is greater than 7.5? The true average years is equal to 7.5? The true average years is not equal to 7.5? Not enough information?

Answer 1

Solution :

Given that,

Population mean = = 7.5

Sample mean = = 7

Sample standard deviation = s = 2

Sample size = n = 100

Level of significance = = 0.05

This is a two tailed test.

The appropriate degrees of freedom for this test is,

df = n - 1 = 100 - 1 = 99

The test statistics,

t = ( - )/ (s/)

= ( 7 - 7.5 ) / ( 2 / 100)

= -2.5

P-value = 0.0141

0.05 > p-value > 0.01

The p-value is p = 0.0141, and since p = 0.0141 <0.05, it is concluded that the null hypothesis is rejected.

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

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population

mean μ is different than 7.5, at the 0.05 significance level.

The true average years is not equal to 7.5