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Week 4 Case Study - EVEN MORE Secret Sauce Of Stats Success

EVEN MORE Secret Sauce of Stats Success

Student’s Name

Institution

Date

Q1: Determine the range of values in which you would expect to find the average weekly sales for the entire sales force in your company 90% of the time, and calculate the following.

Column1

Mean

3966.643077

Standard Error

323.0310322

Median

3907.096154

Mode

#N/A

Standard Deviation

2284.174334

Sample Variance

5217452.388

Kurtosis

-1.285406114

Skewness

0.096968234

Range

7164.865385

Minimum

569.25

Maximum

7734.115385

Sum

198332.1538

Count

50

Confidence Level (95.0%)

649.1551509

Based on the analysis of the average weekly sales of 50 employees, the range values for the expected average weekly sales for the company are 7164.86. However, the mean of average sales is 3966.64, the median is 323.03, and the standard deviation for the average weekly sales is 2284.17. However, the maximum range is 7734.11, and the minimum range is 569.25. The analysis of average weekly sales also indicates that the variance is 5217452.388. However, if the confidence level is increased to 95%, the average weekly sale of the company would increase as well. And based on the analysis of the weekly sales data, the average weekly increased from 541.578 to 649.156. This gives the company an increase of 107.578 of the average weekly sales. But if the company decides to increase the sample size to one hundred and fifty (150), the mean of the sample sales would increase as well and therefore, and the company would be able to get closer to the population.

Q2: Based on the calculated confidence interval for weekly sales on the sample of 50 reps at a 90% confidence level, calculate the following.

Average Weekly Sales

Mean

3966.643077

Standard Error

323.0310322

Median

3907.096154

Mode

#N/A

Standard Deviation

2284.174334

Sample Variance

5217452.388

Kurtosis

-1.285406114

Skewness

0.096968234

Range

7164.865385

Minimum

569.25

Maximum

7734.115385

Sum

198332.1538

Count

50

Confidence Level (90.0%)

541.5779655

The analysis of weekly sales of the rep indicates that the average weekly sale when the confidential level is 90% is 541.578.

Q3: Determine whether there is a statistically different average weekly sale between Sales Rep A and Sales Rep B by doing the following.

Rep B

Mean

4118.866667

Standard Error

278.2098469

Median

4396

Mode

#N/A

Standard Deviation

1523.818089

Sample Variance

2322021.568

Kurtosis

-0.943725802

Skewness

-0.375169677

Range

5290

Minimum

1032

Maximum

6322

Sum

123566

Count

30

Confidence Level (95.0%)

569.003017

Rep A

Mean

4972.266667

Standard Error

368.099649

Median

4703

Mode

#N/A

Standard Deviation

2016.164811

Sample Variance

4064920.547

Kurtosis

-0.836646761

Skewness

-0.293387285

Range

6817

Minimum

1052

Maximum

7869

Sum

149168

Count

30

Confidence Level (90.0%)

625.4480506

The analysis of the weekly sales for rep A and B indicates that there are differences in the mean of weekly sales registered by two sale reps. The average mean for rep A is 4972.27 and rep B registered an average weekly sale of 4118.866667. Therefore, the difference between the two reps is 854.

t-Test: Two-Sample Assuming Equal Variances

Weekly Rep A

Weekly Rep B

Mean

4972.266667

4118.866667

Variance

4064920.547

2322021.568

Observations

30

30

Pooled Variance

3193471.057

Hypothesized Mean Difference

0

df

58

t Stat

1.849552979

P(T<=t) one-tail

0.034737668

t Critical one-tail

1.671552763

P(T<=t) two-tail

0.069475336

t Critical two-tail

2.001717468

The analysis of the weekly sales for rep A and B indicates a unique trend of the sales of the product in a week. Based on the data, it is clear the two sales records for both reps A and B are the same. The analysis established that the P-Value of the two reps A and B is 0.069475. The P- value obtained is higher than the significant value of 0.05 provided, and therefore, the null hypothesis is accepted. This could mean that there is a relationship between weekly sales for Rep A and B. Though rep A made the highest sales compared to rep B, their weekly sales still have some similarities. However, the difference between rep A and B is 854. It means that rep A made a higher sale of 854 than rep B.

Q4: Determine whether this person's average weekly sales are higher than the average weekly sales for the 50 sales reps whose data you used to develop confidence intervals.

z-Test: Two Sample for Means

Average Weekly Sales

Rep A

Mean

3966.643077

4972.266667

Known Variance

0.05

0.05

Observations

50

30

Hypothesized Mean Difference

0

z

-19473.81708

P(Z<=z) one-tail

0

z Critical one-tail

1.644853627

P(Z<=z) two-tail

0

z Critical two-tail

1.959963985

The statistical analysis of the weekly sales for 50 employees and rep B indicates that rep B has a high average sales compared to the average sales for 50 employees. It is established that the average sales for 50 employees are 3966 while the average sales for Rep A are 4972. This means that the difference in average sales between 50 employees and rep B is 1006. It is, therefore; clear that rep A, made a high sales compared to the 50 employees. And thus, in terms of promotion, I can decide to promote rep B for registering higher sales during the month. It is also pointed out that the P- value for the average weekly sales for 50 employees and rep B is 0, P-value =0). The P-Value is, therefore, less than the significant value of 0.05 provided. This means that the null hypothesis is rejected and therefore, there is no direct relationship between the two variables. It could also mean that the average weekly sales of 50 employees and the weekly sales of rep A are not the same.

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