Do Sit-Down Restaurant Franchises and Fast Food Franchises Differ in Stock Price?

What is the test statistic and p-value for the two independent sample t-test comparing the average stock price of sit-down restaurants and fast food restaurants?

The correct answer is: Test Statistic: 1.235 P-Value: 0.1099

Analysis of the Data:

Two Independent Sample T-Test: To compare the average stock prices of sit-down restaurants and fast food restaurants, we conducted a two independent sample t-test. The null hypothesis was that the average stock price of sit-down restaurants is greater than or equal to the average stock price of fast food restaurants (μ1≥μ2), while the alternative hypothesis was that the average stock price of sit-down restaurants is less than the average stock price of fast food restaurants (μ1<μ2).

Calculation of Test Statistic and P-Value:

From the data provided, we calculated the test statistic using the t-test formula: t = ($249.388 - $245.022) / sqrt(($19.1384^2 / 40) + ($15.7443^2 / 58)) This yielded a test statistic of approximately 1.235. To find the p-value, we compared the test statistic to the t-distribution with 38 degrees of freedom and found the p-value to be approximately 0.1099. Conclusion: Based on the results of the t-test, we can conclude that there is not a significant difference in the average stock prices of sit-down restaurants and fast food restaurants. The p-value of 0.1099 indicates that we fail to reject the null hypothesis, suggesting that the average stock prices are not significantly different between the two types of restaurants.

What is the appropriate conclusion based on a p-value of 0.0199 for a hypothesis test comparing the scores of students who study one week before a test to those who study the night before?

The appropriate conclusion is: The average score of students who study one week before a test is significantly different from the average score of students who wait to study until the night before a test.

Analysis of the Data:

Hypothesis Test: The hypothesis test aimed to compare the scores of students who study one week before a test with those who study the night before. The calculated p-value was 0.0199. Conclusion: With a p-value of 0.0199, which is less than the typical significance level of 0.05, we reject the null hypothesis. This indicates that there is enough evidence to suggest that there is a significant difference in the average scores of students who study one week before a test compared to those who wait until the night before. Therefore, the appropriate conclusion is that the average score of students who study one week before a test is significantly different from the average score of students who wait to study until the night before.
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