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: H_{0}: µ_{1} – µ_{2} = 0 H_{a}: µ_{1} – µ_{2} < 0 Here µ_{1} is the population mean of Population 1 and µ_{2} 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 
 Compute the test statistic t
 Compute the degree of freedom for the test statistic t
 What is the rejection rule using the pvalue approach and α=0.05
 What is the pvalue?
 Based on the rejection rule from c., what is your conclusion on the null hypothesis?
 Use the above data to construct a 95% confidence interval for the difference of the population means
 What are the sample mean satisfaction score and the sample standard deviation for the two branches?
 Compute the test statistic t used to test the hypotheses.
 Compute the degree of freedom for the test statistic.
 Can the chain conclude that customer satisfaction level at the two stores is different? Use the criticalvalue approach and α=0.05 to conduct the hypothesis test.
 Construct a 95% confidence interval for the difference of the satisfaction scores for the two stores.
 Perform a statistical test to see whether the average deposits of members before the pilot are different between the two regions.
 Construct a 95% confidence interval for the difference of the two regions in average loans of members before the pilot.
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 
 Compute the test statistic t
 Compute the degree of freedom for the test statistic t
 What is the rejection rule using the critical value approach and α=0.05
 Based on the rejection rule from c., what is your conclusion on the hypotheses
 What is the p value?
 Use the above data to construct a 95% confidence interval for µ_{d}
 Perform a statistical test to see whether the average deposits of members have increased as a result of the pilot
 Perform a statistical test to see whether the average loans of members have increased as a result of the pilot
Source of Variation  Sum of Squares  Degrees of Freedom  Mean Square  F 
Treatment  13456.87  
Error  9456.56  
Total  22913.43 
 Complete the ANOVA table.
 Find the pvalue of the F test statistics
 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
 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 reformat the data, i.e., create a column of data for each of the five branches if you use Excel Data Analysis Addin

 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 Addin, you will need to reformat the data)
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