PART A

1.Consider this hypothesis test: H0: p1 - p2 = < 0

Ha: p1 - p2 > 0

Here p1 is the population proportion of "yes" of Population 1 and p2 is the population proportion of "yes" of Population 2. Use the statistics data from a simple random sample of each of the two populations to complete the following: (8 points)

Population 1 Population 2

Sample Size (n) 500 700

Number of "yes" 400 560

a.Compute the test statistic z.

b.What is the p-value?

c.Should H 0 be rejected? Use the p-value and a level of significance of 0.05to justify your answer.

d.Use the above data to construct a 95% confidence interval for p1 - p2

2.Use the data in BUSINESS Bank Dateset. XL to answer this question. (4 points each; 8 Points in total)

a.Perform a statistical test to see whether the proportion of members who would recommend the Bank to their family and friends have increased because of the change.

b.Construct a 99% confidence interval for the difference of the proportions, before and after the change, of members who would recommend the Bank to their family and friends.

3.A national retailer has completed an internal survey on its social media strategy. The key question in the survey is whether the stores managers think that the recently- launched social media strategy is effective. The following is the output of a statistical analysis of the data:

Social Media Strategy is effective

Store Managers No Yes

West Region 20 35

Central Region 15 35

East Region 40 55

Based on this output, can the retailer conclude that the opinion of the store managers on the whether the recently-launched social media strategy is effective is dependent on which region they belong to? Use a chi square test and a level of significance of 0.05. (4 points)

PART B

1.The following output was obtained from a regression analysis of the dependent variable Rating and an independent variable Price. (10 points)

ANOVA

df SS MS F

Regression 1 372.707 372.707 42.927

Residual 15 130.234 8.682

Total 16 502.941

Coefficients Standard Error t Stat P-value

Intercept 45.623 3.630 12.569 0.000

Price 0.107 0.016 6.552 0.000

a.Use the critical value approach to perform an F test for the significance of the linear relationship between Rating and Price at the 0.05 level of significance.

b.Calculate the coefficient of determination.

c.What percentage of the variability of Rating can be explained by its linear relationship with Price? What is the sample correlation coefficient?

d.What is the estimated regression equation?

e.Use the p-value approach to perform a t test for the significance of the linear relationship between Price and Rating at the 0.05 level of significance.

2.The estimated regression equation for a model involving two independent variables and 65 observations is:

yhat = 55.17+1.2X1 -0.163X2

Other statistics produced for analysis include: SSR = 12370.8, SST = 35963.0, Sb1 = 0.33, Sb2 = 0.20. (16 points)

a.Interpret b1 and b2 in this estimated regression equation

b.Predict y when X1 = 65 and X2 = 70.

c.Compute R-square and Adjusted R-Square.

d.Comment on the goodness of fit of the model.

e.Compute MSR and MSE.

f.Compute F and use it to test whether the overall model is significant using a p-value ( = 0.05).

g.Perform a t test using the critical value approach for the significance of 1.Use a level of significance of 0.05.

h.Perform a t test using the critical value approach for the significance of 2.Use a level of significance of 0.05.