A study was conducted to see if an advertisement campaign would increase market share for Sanka instant decaffeinated coffee (R. Grover and V. Srinivasan, J. Marketing Research , vol. 24, 1987, pp. 139€“153). Subjects who use instant decaffeinated coffee were asked which brand they bought last. They were asked this before the campaign and after it. The results are shown in the table.
a. Estimate the population proportion choosing Sanka for the
(i) First purchase
(ii) Second purchase.
b. Explain how each proportion in part a can be found as a sample mean and how the estimated difference of population proportions is a difference of sample means.
c. The table also shows results of a confidence interval for the difference between the population proportions. Explain how to interpret it.

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Two Purchases of Coffee Second Purchase Sanka Other Brand First Purchase Sanka Other brand 49 261 StDev Difference 541 0.050 0.478 155 76 N Mean SE Mean 0.021 95% CI for mean difference: (0.010, 0.090 )