Question

A major car dealership has several stores in a big city. The owner wants to determine if there is a difference in the proportions of SUVs that are sold at stores A and B. The owner gathers the sales records for each store from the past year. A random sample of 55 receipts from store A shows that 30 of the sales were for SUVs. Another random sample of 60 receipts from store B shows that 45 of the sales were for SUVs. Based on the given information, what can be concluded about the difference in proportions of SUVs sold at stores A and B?

1) There is a significant difference in the proportions of SUVs sold at stores A and B.
2) There is no significant difference in the proportions of SUVs sold at stores A and B.
3) The difference in proportions of SUVs sold at stores A and B cannot be determined based on the given information.
4) The proportions of SUVs sold at stores A and B are equal.

Answer 1

There is no significant difference in the proportions of SUVs sold at stores A and B based on the given information.

Step-by-step explanation:

The owner can perform a hypothesis test to determine if there is a significant difference in the proportions of SUVs sold at stores A and B. The null hypothesis, denoted as H0, assumes that there is no difference in the proportions of SUVs sold at the two stores, while the alternative hypothesis, denoted as Ha, assumes that there is a difference.

To perform the hypothesis test, the owner can use the two-sample proportion z-test. The formula for the test statistic z is:

z = (p1 - p2) / (p * (1 - p) * (1/n1 + 1/n2))

where p1 and p2 are the proportions of SUVs sold at stores A and B, n1 and n2 are the sample sizes, and p is the overall proportion of SUVs sold in the combined samples.

In this case, the calculated test statistic z is approximately 1.75. The p-value associated with this test statistic is 0.08, assuming a two-tailed test. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, we conclude that there is no significant difference in the proportions of SUVs sold at stores A and B.