BUS201: Descriptive Analysis & Create a new variable for each company - Statistics Assessment Answers

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You are asked to advise a client who is looking into purchasing a cleaning company. It has two Sydney companies in mind (codenamed A and B). The Excel Spreadsheet Prospectives contains the data with the following two variables

Crews: the number of crews sent to each job.

Rooms: the number of rooms cleaned at each job.

As part of its investigation your client is asking you to analyse the data on the two companies which it has obtained and to prepare a report into the following points.

Question 1.Descriptive analysis

1. Prepare appropriate summary statistics on each variable and comment on each of these.
2. Use Excel to draw up the histograms of number of rooms cleaned for each company. Comment on the shape of the histograms and compare between the two companies.
3. Use a PivotTable to summarise the performance of the number of crews by looking at the sum of rooms cleaned by each crew size for each company. Compare the two companies by using the output of the pivot table.

Question 2.

Create a new variable for each company, viz., the ratio of

The number of Offices cleaned

Number of crews .

Call these variables OCA and OCB

Your client wants to know which company has the lower mean OC (why does he want this statistic?). Other information suggests that company B might have the higher mean. Test this hypothesis at 5% level of significance. Set out your analysis for this fully. What can be recommended to your client?

Question 3.

For the company chosen in 2, your boss wants you to fit a simple linear regression model to the data. Incorporate appropriate output in your report.

y = Number of Rooms cleaned

x = Number of Crews

1. Justify the choice of explanatory and dependent variables.
2. Estimate the regression equation between these variables.
3. State and interpret the slope coefficient
4. State and interpret the R2 value from this.

Iii Give a final summary of your findings from this regression.

Question 1

The descriptive statistics is given below

The mean number of crews sent to each job in company A is 8.88 crews with a standard deviation of 4.83 crews. The median number of crews sent to each job in company A is 9. This indicates that, nearly 50% of the sample number of crews sent to each job falls below 9 and 50% of the sample number of crews sent to each job falls above 9. The minimum and maximum recorded number of crews sent to each job in Company A is 2 and 16 respectively.

The mean number of rooms cleaned to each job in company A is 34.44 crews with a standard deviation of 19.34 crews. The median number of rooms cleaned to each job in company A is 36. This indicates that, nearly 50% of the sample number of rooms cleaned to each job falls below 36 and 50% of the sample number of rooms cleaned to each job falls above 36. The minimum and maximum recorded number of rooms cleaned to each job in Company A is 6 and 78 respectively.

The mean number of crews sent to each job in company B is 8.81 crews with a standard deviation of 4.76 crews. The median number of crews sent to each job in company B is 8. This indicates that, nearly 50% of the sample number of crews sent to each job falls below 8 and 50% of the sample number of crews sent to each job falls above 8. The minimum and maximum recorded number of crews sent to each job in Company B is 2 and 16 respectively.

The mean number of rooms cleaned to each job in company B is 38.56 crews with a standard deviation of 18.97 crews. The median number of rooms cleaned to each job in company B is 44. This indicates that, nearly 50% of the sample number of rooms cleaned to each job falls below 41 and 50% of the sample number of rooms cleaned to each job falls above 41. The minimum and maximum recorded number of rooms cleaned to each job in Company B is 10 and 82 respectively.

1. Histograms

Histogram for Number of rooms cleaned – Company A

Going through the histogram of the number of rooms cleaned at each job in Company A, it is found that the distribution of number of rooms cleaned at each jobs follows normal distribution approximately

Histogram for Number of rooms cleaned – Company B

Going through the histogram of the number of rooms cleaned at each job in Company B, it is found that the distribution of number of rooms cleaned at each jobs follows normal distribution approximately

1. Pivotal Table

The mean comparison of number of crews and number of rooms cleaned at each job between two companies is given below

On comparing the mean number of crews sent to each job between Company A and Company B, we see that Company B sends relatively lesser number of crews when compared to that of Company A

On comparing the mean number of rooms cleaned to each job between Company A and Company B, we see that Company B crews cleans relatively higher number of crews when compared to that of Company A

Question 2

In order to determine whether there is a significant mean difference in OC between Company A and company B, we perform independent sample t test. The null and alternate hypotheses are given below

Null Hypothesis: H0: µOCA = µOCB

That is, the mean OC do not differ significantly between company A and company B

Alternate Hypothesis: H0: µOCA ? µOCB

That is, the mean OC differ significantly between company A and company B

Level of Significance: Let the level of significance be ? = 0.05

Test Statistic

The t test statistic is

t=x1-x2s1n1+1n2

The table given below shows the workings of t test statistic

The value of t test statistic is -3.622 and its corresponding p – value is 0.000462. Since the p – value of t test statistic falls below 0.05, there is sufficient evidence to reject the null hypothesis at 5% level of significance. Therefore, we conclude that the mean OC differ significantly between company A and company B. Going through the mean values, we see that the mean OCB (mean = 4.735, Std dev = 1.217) is significantly high when compared to that of OCA (mean = 3.953, Std dev = 0.94), indicating that the company A has the lower mean OC. Therefore, we can recommend Company A to the client

Question 3

The regression model to predict number of rooms cleaned using number of crews as independent variable is given below

The regression model is

Number of Rooms = b0 + b1 * Number of Crews

The regression output is given below

The regression equation is

Number of Rooms = 1.575 + 3.701 * Number of Crews

The independent variable is number of crews and the dependent variable is number of rooms cleaned. Here, we wishes to predict the number of rooms cleaned using the number of crews employed at each job.

1. The coefficient of slope is 3.701. This indicates that when the number of crews sent to each job increases by one crew, then the number of rooms cleaned will increase by 3.701 rooms. The t test for significance of slope is used to test whether the slope is a significant predictor of dependent variable. The value of t test statistic is 16.91 and its corresponding p – value falls below 0.05, indicating that the independent variable number of crews sent to each job is a significant predictor of number of rooms cleaned at each job
2. The coefficient of determination is 0.8563. This indicates that, the variation of about 85.63% of dependent variable number of rooms is explained by the regression model and the remaining 14.37% left unexplained

iii.

The value of f test statistic is 285.9485 and its corresponding p – value falls well below 0.05, indicating that the regression model is good fit in predicting the number of rooms cleaned at each job. In addition, we see that there exists a strong positive linear relationship between number of crews and number of rooms cleaned (Correlation Coefficient = 0.9253). Thus, we can conclude that the independent variable number of crews at each job is a significant predictor of number of rooms cleaned