Question

Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

A random sample of  100 people from region A and a random sample of  100 people from region B were surveyed about their grocery-shopping habits. From the region A sample,  16 percent of the people indicated that they shop for groceries online. From the region B sample, 24 percent of the people indicated that they shop for groceries online.

At the significance level of  α=0.05, do the data provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries? Complete the appropriate inference procedure to support your answer.

Answer 1

given data are:-

From the region A the sample proportion ()of the people indicated that they shop for groceries online = 0.16

From the region B the sample proportion ()of the people indicated that they shop for groceries online = 0.24

the pooled proportion be:-

hypothesis:-

test statistic:-

p value be:-

[ in any blank cell of excel type =NORMSDIST(-1.414) press enter]

decision:-

p value = 0.1574 > 0.05 (alpha)

so, we fail to reject the null hypothesis.

conclusion:-

the data do not provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries at 0.05 level of significance.

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