Question

Pat is the manager of a real estate group that is part of a larger real estate company. Here are the total number of home sales from 2019 for all the agents at the entire company.

15
20
3
5
6
8
9
10
10
4
5
6
9
4
3
14
2
5
8

Pat wants to know if her own real estate group, which has 4 agents (the sample, in this case), has sold more homes than the rest of the company (the population). Your job is to tell me if these four agents (agents A, B, C, and D) differ in number of home sales from the population (the entire company). Remember that you need to calculate the population standard deviation first!

Home Sold per Agent

Agent	Number of homes sold in 2019
A	10
B	8
C	4
D	6

Your job is to determine if this sample (The average of agents A, B, C, and D) differ significantly from what you would expect given the population (the rest of the company).

1. The value needed to reject the null hypothesis (the critical value) is ___________.

Group of answer choices

2.10

3.25

1.96

0.05

2. Does the obtained value exceed the critical value (that is, is the obtained value larger than the critical value)?

Group of answer choices

No

Yes

3. Based on your answer to the previous question, the decision is to ____________

Fail to reject the null hypothesis

Reject the null hypothesis

4. Write up your results as you would see it in a results section of an empirical research paper:

Answer 1

First we have to calculate the population mean and population standard deviation from the given data

Following commands can be used to calculate the mean and standard deviation:

Mean : (=average)
Standard deviation: (=stdev.p)

The sample mean would be: (10+8+4+6)/4 = 7

1. The value needed to reject the null hypothesis (the critical value) is ___1.96________.

Group of answer choices

2.10

3.25

1.96

0.05

2.

The obtained value can be calculated as follows:

Therefore, the obtained value is -0.3

2. Does the obtained value exceed the critical value (that is, is the obtained value larger than the critical value)?

Group of answer choices

No

Yes

3. Based on your answer to the previous question, the decision is to ____________

Fail to reject the null hypothesis

Reject the null hypothesis

4.

The mean number of sales of 4 agents is same as the mean number of sales of the population. z = -0.3, p = 0.7642