Question

PLEASE HELP! Z-test or T-test? Give a full explanation please!

A researcher wants to compare the email use of the employees at one company to the corresponding population. Data is collected on the number of emails received by the company's employees. It will be necessary to use this sample data, as well as population data to determine if there is a significant difference between both.

Population

Mean number of emails: 25

Standard deviation: 3

Sample

Mean number of emails: 20

Total employees: 100

A researcher wants to compare the number of vehicles owned by families in one location to the larger population. Data is collected on the number of vehicles owned by each family. It will be necessary to use this sample data, as well as population data to determine if there is a significant difference between them.

Population

Mean number of vehicles: 4

Sample

Mean number of vehicles: 3

Standard deviation: 1

Sample size: 100

Create a report of approximately 1-2 pages in which you address the following:

Identify the test you selected for each situation.

Explain why it was the appropriate test.

Present the results of each test.

Explain whether or not a significant difference was found between the sample and the population.

Answer 1

(1)

Since the population standard deviation is known, we use z- test

Data:      

n = 100     

μ = 25     

σ = 3     

x-bar = 20     

Hypotheses:     

Ho: μ = 25     

Ha: μ ≠ 25     

Decision Rule:     

α = 0.05     

Lower Critical z- score = -1.959963985    

Upper Critical z- score = 1.959963985    

Reject Ho if |z| > 1.959963985    

Test Statistic:     

SE = s/√n = 3/√100 = 0.3    

z = (x-bar - μ)/SE = (20 - 25)/0.3 = -16.66666667   

p- value = 0     

Decision (in terms of the hypotheses):    

Since 16.66666667 > 1.959963985 we reject Ho and accept Ha

Conclusion (in terms of the problem):    

There is sufficient evidence of a significant difference between the two means.