Question

A potential electronic grocer analyzed the market to be profitable, with an average order exceeding $85. From a random sample (X = 89.27, s = 17.30, n = 85, α = 0.05), can we infer that an e-grocery store will be profitable in this city?

a. Yes
b. No

Answer 1

To determine whether an e-grocery store will be profitable in a city, conduct a one-sample t-test using the provided sample data and hypotheses. Calculate the test statistic and determine the p-value to make a conclusion. In this case, we reject the null hypothesis and infer that the e-grocery store will be profitable in the city. The answer is a. Yes.

Step-by-step explanation:

To determine whether an e-grocery store will be profitable in a city, we can perform a hypothesis test using the given sample data. The null hypothesis, H0, is that the average order is not greater than $85, while the alternative hypothesis, Ha, is that the average order is greater than $85. We can use a one-sample t-test to test this hypothesis.

First, we calculate the test statistic t by using the formula: t = (X - μ) / (s / √n), where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size. Substituting the given values, we have t = (89.27 - 85) / (17.30 / √85) = 1.94.

Next, we determine the p-value associated with the calculated test statistic. Using a t-distribution table or a statistical calculator, the p-value is found to be approximately 0.0306. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.

Therefore, based on the sample data, we can infer that the e-grocery store will be profitable in this city.