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. To complete this question review the chart located on #16 pg. 307.

Table or chart are not available.

To determine if the results support the researcher's theory, we will conduct a hypothesis test using the steps of hypothesis testing. Here are the steps:

Step 1: State the hypotheses.
In this problem, the null hypothesis (H0) would be that there is no difference in hearing ability between individuals who eat a large meal and those who eat a small meal. The alternative hypothesis (Ha) would be that people who eat a large meal have better hearing ability.

Step 2: Set the significance level.
The significance level, denoted as alpha, is set at 0.05. This means we want a 5% chance of making a Type I error, which is rejecting the null hypothesis when it is true.

Step 3: Compute the test statistic.
In this problem, since we have two independent groups (large meal and small meal), we can use a two-sample t-test. The formula for the test statistic is:
t = (mean1 - mean2) / (sqrt(s1^2/n1 + s2^2/n2))

where mean1 and mean2 are the means of the two groups, s1 and s2 are the standard deviations, and n1 and n2 are the sample sizes.

Step 4: Determine the critical value or p-value.
To determine the critical value, we compare the test statistic to the t-distribution with (n1 + n2 - 2) degrees of freedom at the 0.05 significance level. The critical value is the t-value at the rejection region.

If using a p-value approach, we compare the p-value to the significance level. If the p-value is less than the significance level, we reject the null hypothesis.

Step 5: Make a decision.
If the test statistic falls within the rejection region or if the p-value is less than the significance level, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Step 6: Interpret the results.
If we reject the null hypothesis, we can conclude that there is evidence to suggest that people who eat a large meal have better hearing ability.

To complete the question, you will need to review the chart on Pg. 307, which contains the hearing ability scores for the individuals who ate a large meal and those who ate a small meal. Compute the test statistic and determine the critical value or p-value to make a decision.

Additionally, sketching the distributions involved (large meal and small meal) can help visualize the data and the comparisons being made. You can plot histograms or box plots for each group and observe any differences in their distributions.

Note: Due to the limitations of text-based communication, I am unable to view and analyze specific charts or data.