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, review a chart that reference to this question

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

Step 1: State the hypotheses
- Null hypothesis (H0): There is no difference in hearing ability between those who eat a large meal and those who eat a small meal.
- Alternative hypothesis (Ha): People who eat a large meal have better hearing ability compared to those who eat a small meal.

Step 2: Set the significance level
The significance level, denoted by α, is the threshold at which we will reject the null hypothesis. In this case, the significance level is 0.05, which is a common choice in hypothesis testing.

Step 3: Collect and summarize the data
The table given provides the hearing ability scores for the individuals who ate a large meal and those who ate a small meal.

Step 4: Analyze the data and calculate the test statistic
To analyze the data, we can compare the means of the two groups using a t-test. Calculate the mean and standard deviation for each group.
- Large meal group: Mean = (sum of scores)/(number of individuals), Standard deviation = √((∑(score - mean)^2)/(n-1))
- Small meal group: Mean = (sum of scores)/(number of individuals), Standard deviation = √((∑(score - mean)^2)/(n-1))

Step 5: Determine the critical value or p-value
Using the t-distribution, with the degrees of freedom calculated as the sum of the sample sizes minus 2 (n1 + n2 - 2), find the critical t-value for a two-tailed test at the chosen significance level (α=0.05). Alternatively, calculate the p-value associated with the test statistic.

Step 6: Make a decision
- If the test statistic falls within the critical region (reject H0), then we have evidence to support the alternative hypothesis.
- If the test statistic does not fall within the critical region (fail to reject H0), then we do not have sufficient evidence to support the alternative hypothesis.

Step 7: Interpret the results
Based on the decision made in Step 6, interpret the results in the context of the problem and make conclusions.

In order to complete steps (b) and (c), a chart or additional information is needed, which is not provided in this question.