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BUSI1013:Statistics for Business

BUSI1013:Statistics for Business nless otherwise specified, you should use 0,05 as the level of significance 1. Consider this hypothesis test: H0: µ1 – µ2 = 0 Ha: µ1 – µ2 < 0 Here µ1 is the population mean of Population 1 and µ2 is the population mean of Population 2. Use the statistics summarized from a simple random sample of each of the two populations to complete the following: (12 Points)

Population 1

Population 2
Sample Size ( n)

50

60
Sample mean (xbar)

24.5

25.9
Sample standard deviation (s)

5.43

7.21
  1. Compute the test statistic t
  2. Compute the degree of freedom for the test statistic t
  3. What is the rejection rule using the p-value approach and α=0.05
  4. What is the p-value?
  5. Based on the rejection rule from c., what is your conclusion on the null hypothesis?
  6. Use the above data to construct a 95% confidence interval for the difference of the population means
Note that the population standard deviations are not known and therefore you cannot use the formula in Section 10.1. Use those in Section 10.2 instead. 2. Responses from a customer satisfaction survey for two stores of a local hardware chain were recorded in the attached BUSI1013-2 Independent Samples A.xls file. These responses, in the form of a satisfaction score, are taken from a random sample of customers who shopped recently at the two stores and are recorded on the scale of 1 to 10. The chain wants to use this data to test the research (alternative) hypothesis that the mean satisfaction score for the two branches is not the same. The null hypothesis is that the mean satisfaction score for the two branches is the same (10 Points)
  1. What are the sample mean satisfaction score and the sample standard deviation for the two branches?
  2. Compute the test statistic t used to test the hypotheses.
  3. Compute the degree of freedom for the test statistic.
  4. Can the chain conclude that customer satisfaction level at the two stores is different? Use the critical-value approach and α=0.05 to conduct the hypothesis test.
  5. Construct a 95% confidence interval for the difference of the satisfaction scores for the two stores.
3. Use BUSI1013-Case.xls and the description of this file in Assignment 1 to answer this question. (4 Points for each part; 8 Points total)
  1. Perform a statistical test to see whether the average deposits of members before the pilot are different between the two regions.
  2. Construct a 95% confidence interval for the difference of the two regions in average loans of members before the pilot.
4. Consider this hypothesis test: H0: µd = 0 Ha: µd > 0 Here µd is the mean difference of two measures in a population. Using the data collected from a simple random sample of the population to complete the following: (12 Points)

Sample Unit

Measure 1

Measure 2

Difference

1

15.6

19.2

3.6

2

17.3

13.6

-3.7

3

16.2

14.3

-1.9

4

20.4

21.9

1.5

5

17.3

19.7

2.4

6

21.5

20.3

-1.2

7

 15.4

17.2

 1.8

8

18.2

20.4

2.2

9

 22.8

29.8

 7

10

24.1

29.7

5.6

11

 24.8

26.3

1.5

Sample Mean

1.709

Sample Standard Deviation

3.135
  1. Compute the test statistic t
  2. Compute the degree of freedom for the test statistic t
  3. What is the rejection rule using the critical value approach and α=0.05
  4. Based on the rejection rule from c., what is your conclusion on the hypotheses
  5. What is the p value?
  6. Use the above data to construct a 95% confidence interval for µd
5. Use BUSI1013-Case.xls and the description of this file in Assignment 1 to answer this question. (4 Points for each part; 8 Points total)
  1. Perform a statistical test to see whether the average deposits of members have increased as a result of the pilot
  2. Perform a statistical test to see whether the average loans of members have increased as a result of the pilot
6. In a completely randomized design, eight experimental units were used for each of the three levels of the factor. (3 Points for Part a, 1 Point for Part b, 2 Points for Part c, Total 6 Points)
Source of Variation Sum of Squares Degrees of Freedom Mean Square F
Treatment 13456.87
Error 9456.56
Total 22913.43
  1. Complete the ANOVA table.
  2. Find the p-value of the F test statistics
  3. Use the critical value approach and α=0.05 to test whether or not the population means for the four levels of the factors are the same
7. Use BUSI1013-Case.xls and the description of this file in Assignment 1 to answer this question. (4 Points for each part; 8 Points total)
  1. Perform a statistical test to see whether the average deposits of members after the pilot is the same among the five branches. You will need to re-format the data, i.e., create a column of data for each of the five branches if you use Excel Data Analysis Add-in
    1. Perform a statistical test to see whether the average increase in loans of members is the same among the five branches. (You need to create a new variable called average increase in loans. Also, if you use the Excel Data Analysis Add-in, you will need to re-format the data)
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