Question

A powder diet is tested on 49 people and a liquid diet is tested on 36 different people. The objective is to determine whether the liquid diet yields a different average weight loss than the powder diet. The powder diet group had an average weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had an average weight loss of 45 pounds with a standard deviation of 14 pounds. Conduct a hypothesis test at the 5

Answer 1

To conduct a hypothesis test to determine if the liquid diet yields a higher mean weight loss than the powder diet, we can use a two-sample t-test. The steps to conduct the test include formulating the null and alternative hypotheses, choosing the significance level, calculating the test statistic, determining the critical value, making a decision, and interpreting the result.

Step-by-step explanation:

The question asks for a hypothesis test to determine if the liquid diet yields a higher mean weight loss than the powder diet. We can use a two-sample t-test to compare the means of the two groups. Here are the steps to conduct the hypothesis test:

1. Step 1: Formulate the null and alternative hypotheses: The null hypothesis (H0) is that there is no difference in mean weight loss between the two diets. The alternative hypothesis (Ha) is that the liquid diet yields a higher mean weight loss than the powder diet.
2. Step 2: Choose the significance level: The question mentions conducting the test at the 5% level, so the significance level (α) is 0.05.
3. Step 3: Calculate the test statistic: In this case, we can use the two-sample t-test formula to calculate the test statistic. The formula is:
4. Step 4: Determine the critical value: With a significance level of 0.05 and degrees of freedom calculated based on the sample sizes, we can find the critical value from the t-distribution table or use statistical software.
5. Step 5: Make a decision: Compare the test statistic to the critical value. If the test statistic is greater than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
6. Step 6: Interpret the result: If we reject the null hypothesis, it means we have enough evidence to support the claim that the liquid diet yields a higher mean weight loss than the powder diet. If we fail to reject the null hypothesis, it means we do not have enough evidence to support the claim.