Practice Problem #16 pg. 307: A researcher theorized that people can hear better when they have just eaten a large meal. Six individuals were randomly assigned to eat either a large meal or a small meal. After eating the meal, their hearing was tested. The hearing ability scores (high numbers indicate greater ability) are given in the following table. Using the .05 level, do the results support the researcher’s theory? (a) Use the steps of hypothesis testing, (b) sketch the distributions involved. (c) Does not need to be completed in this assignment

Since we don't have the table, we cannot accurately respond. Copy and paste may not work.

To determine whether the results support the researcher's theory, we need to conduct a hypothesis test. Here are the steps to follow:

(a) Steps of hypothesis testing:
1. State the null hypothesis (H0) and the alternative hypothesis (Ha):
- Null hypothesis (H0): There is no difference in hearing ability between individuals who eat a large meal and those who eat a small meal.
- Alternative hypothesis (Ha): Individuals who eat a large meal have better hearing ability than those who eat a small meal.

2. Set the significance level (α): The question states to use a significance level of .05.

3. Collect and analyze the data: In this case, we have the hearing ability scores for six individuals who were randomly assigned to either a large meal or a small meal.

4. Determine the test statistic: Since we have two groups (large meal and small meal), we can use a two-sample t-test to compare their means.

5. Calculate the p-value: Compute the p-value associated with the test statistic. It represents the probability of obtaining the observed or more extreme results if the null hypothesis is true.

6. Make a decision: Compare the p-value to the significance level. If the p-value is less than the significance level (α), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

7. State a conclusion: Based on the decision made in step 6, state whether the results support the researcher's theory.

(b) Sketching the distributions involved:
To sketch the distributions, we would need the actual data (hearing ability scores) for both the large meal and small meal groups. Unfortunately, the data is not provided in the question, so we cannot sketch the distributions.

(c) This part does not need to be completed in this assignment.

Please note that without the actual data, we cannot perform the calculations needed for the hypothesis test. Make sure to gather the hearing ability scores for both groups to carry out the analysis.