Question

Part 1: Hypothesis Testing (25 points)
Step 1: Suppose you are asked to conduct a hypothesis test on the population mean. What type of hypothesis test would you use? What assumptions do you need to make about the process when you are conducting a hypothesis test on the population mean in order for your results to be valid?

This needs to be at least one (1) paragraph in length. Note a paragraph contains at least three complete sentences. Watch your spelling and grammar.
Step 2: Go to the Hypothesis Testing worksheet in the Project_Data Excel file. Press the button:

Press the Button to Generate the Data. This will populate column A with data. Please note you must press this button. Do not copy data from another place. I will be checking to see if you indeed pressed the button to generate your own unique data for the project!

303.71
255.53
341.58
270.29
200.3
223.77
239.01
212.76
236.81
375.71
328.05
336.41
243.86
292.79
383.37
336.96
241.87
258.06
306.95
321.36
208.52
389.77
392.05
200.59
331.47
369.3
371.62
258.65
329.26
398.28
351.83
360.82
385.59
382.99
248.91
367.23
284.7
348.98
333.24
289.53
211.11
249
347.68
328.02
398.58
208.1
277.1
346.8
363.28
305.05
337.3
316.38
318.3
283.95
390.98
385.4
292.28
234.16
267.16

Step 3: Once the button is pressed and the data generated, you will be asked to conduct a hypothesis test. Note, this is sample data that has been generated. Assume the population standard deviation is unknown and the data is from a normally distributed population.

Conduct a two tailed hypothesis test for the population mean. You will need to provide the following:
1) Pick a hypothesized value (what you believe the population mean may be. Don’t use the sample mean for the hypothesized value). State your null and alternative hypotheses. Use a two tailed test.
2) Determine the test statistic
3) Determine the p-value
4) Determine the critical values for the hypothesis test.
5) Clearly explain whether one should reject or not reject the null hypothesis at a 5% level of significance. Explain your reasoning.

Possible Points:
• Assumptions discussion: 6 possible points
• Null and alternative hypotheses: 4 possible points
• Test statistic: 3 possible points
• p-value: 3 possible points
• Critical values 3 possible points
• Conclusions: 6 possible points

Part 2: Simple Linear Regression (30 points)
Scenario: You are curious to see if there is a possible relationship between the number of promotions and total sales.

Step 1: Go to the Regression worksheet in the Project_Data Excel file. Press the button:
Press the Button to Generate the Data. This will populate columns E and F with data. Please note you must press this button. Do not copy data from another place. I will be checking to see if you indeed pressed the button to generate your own unique data for the project!

Step 2: Once the button is pressed and the data generated, you will be asked to provide the following:
• Create a scatter diagram. Be sure to include axis titles on your graph and a trend line with the equation.

Number of Promotions	Total Sales
0	2836
1	2896
2	2540
1	1593
13	2139
15	2455
13	1661
10	2263
9	1978
14	2189

• Run a linear regression using Excel’s Data Analysis regression tool. Construct the linear regression equation and determine the predicted total sales value if the number of promotions is 6. Is there a significant relationship? Clearly explain your reasoning using the regression results.

• Possible points:
Scatter diagram: 6 possible points
Regression:
• Regression line: 3 possible points
• Predicted value: 3 possible points
• Significance discussion: 6 possible points
• Excel Data Analysis Regression: 12 possible points

Answer 1

Step 1:

I would use either "one sample Z-test for population mean" or "one sample t-test for population mean". Z-test is used if the sample size, n is large enough (​​​​​​) by assuming that the population distribution is normal and population standard deviation is known (if not given, it is approximated by the sample standard deviation). t-test is used if the sample size, n is small (<30) by assuming that the population distribution is normal or approximately normal.

n30

Step 2: Hypothesis testing using Z-test (since n =59 > 30):

1)

Hypothesized value (hypothesized population mean) is: $\mu0$ =300

Null hypothesis(H0):

The population mean is not significantly different from 300. ​​​​​​

300

Alternative hypothesis(H1):

The population mean is significantly different from 300. ​​​​​​

ルチ300

(two tailed test).

($\mu$ =Population mean).

2) Test statistic(Z):

Z =(
X-0)/(s/n
=(308.0188 - 300)/(59.9083/
V59
​​​​​​) =1.028

3) p-value:

The p-value for Z =1.028, for a two-tailed test is: p-value =0.304

4) Critical values for the hypothesis test:

For a two-tailed Z-test, at 5% significance level, the critical values are: $\pm$1.96

5)

One should not reject the null hypothesis at a 5% level of significance because p-value is greater than 0.05 significance level (0.304 > 0.05)

Thus, we do not have enough evidence to claim that the population mean, $\mu$ is significantly different from 300.