10.15 A psychologist theorized that people can hear better when the 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 below. Using the 0.05 level, do the results support the psychologist’s theory

H0 is u = u1

H1 is u not equal to u2

But you have not specified the results of the test to check the hypothesis with!?!

This experiment (as you state it) is faulty. You need to test hearing before and after eating to note the effect of the meals on hearing.

Also the scores are not given. For most, copy and paste does not work.

To determine whether the results support the psychologist's theory, we need to conduct a hypothesis test. In this case, we are comparing the hearing ability scores between individuals who ate a large meal and those who ate a small meal.

Let's set up the hypothesis statements:
- Null hypothesis (H0): People's hearing ability is not affected by the size of the meal.
- Alternative hypothesis (Ha): People's hearing ability is significantly better when they have eaten a large meal.

We can use a two-sample t-test to compare the means of the two groups. Before conducting the t-test, let's calculate some summary statistics:

Group with large meal:
- Sample size (n1) = 3 (assuming large meal)
- Mean (x̄1) of the hearing ability scores = sum of scores / n1
- Variance (s1^2) of the hearing ability scores = sum of (score - x̄1)^2 / (n1 - 1)

Group with small meal:
- Sample size (n2) = 3 (assuming small meal)
- Mean (x̄2) of the hearing ability scores = sum of scores / n2
- Variance (s2^2) of the hearing ability scores = sum of (score - x̄2)^2 / (n2 - 1)

Next, we calculate the t-statistic using the formula:

t = (x̄1 - x̄2) / sqrt((s1^2 / n1) + (s2^2 / n2))

Finally, using the t-statistic, we can determine the p-value associated with the test statistic. With the obtained p-value, we can compare it to the significance level (0.05 in this case) to make our decision.

If the p-value is less than the significance level (0.05), we reject the null hypothesis and conclude that there is evidence to support the psychologist's theory. Conversely, if the p-value is greater than the significance level, we fail to reject the null hypothesis.

By following these steps and calculating the necessary statistics, you can determine whether the results support the psychologist’s theory.