A major appliance store is considering introducing an online shopping service. The service will be implemented if more than 40% of Internet users purchase through this medium. 300 users were interviewed and 170 indicated that they use the Internet to make purchases. With a significance of 0.13, do the data indicate that the service should be implemented?

To determine whether the data indicate that the service should be implemented, we can perform a hypothesis test using the given information. In this case, we'll use a hypothesis test for a population proportion. Here are the steps: Step 1: Set up Hypotheses The null hypothesis (H0) is that the proportion of Internet users who purchase through the online shopping service is less than or equal to 40%: H0: p ≤ 0.40 The alternative hypothesis (Ha) is that the proportion is greater than 40%: Ha: p > 0.40 Step 2: Collect Data From the information given: Number of Internet users surveyed (n) = 300 Number of users who indicated they use the Internet to make purchases (x) = 170 Step 3: Choose a Significance Level The significance level (alpha) is given as 0.13. This is the probability of making a Type I error, which is the probability of rejecting the null hypothesis when it is actually true. Step 4: Calculate the Test Statistic We will calculate the test statistic using the sample proportion (p̂) and the null hypothesis proportion (p0): p̂ = x / n = 170 / 300 = 0.5667 Now, we calculate the standard error (SE) of the sample proportion: SE = sqrt((p0 * (1 - p0)) / n) SE = sqrt((0.40 * 0.60) / 300) ≈ 0.0283 Now, we can calculate the z-score: z = (p̂ - p0) / SE = (0.5667 - 0.40) / 0.0693 ≈ 5.8905 Step 5: Determine the Critical Value Since we have a significance level of 0.13 and this is a one-tailed test (greater than), we need to find the critical z-value from the standard normal distribution. You can use a standard normal table or calculator to find the z-value corresponding to a cumulative probability of 1 - 0.13 = 0.87. For a significance level of 0.13, the critical z-value is approximately 1.1503. Step 6: Make a Decision Compare the calculated z-value (5.8905) to the critical z-value (1.1503). Since the calculated z-value (5.8905) is greater than the critical z-value (1.1503), we reject the null hypothesis (H0). Step 7: Conclusion Since we have rejected the null hypothesis, we have evidence to suggest that more than 40% of Internet users purchase through the online shopping service. Therefore, based on the data and the significance level of 0.13, it appears that the service should be implemented.