T-test independent that people can hear better after having eaten a large meal
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.
Big Meal Group Small Meal Group
Subject Hearing Subject Hearing
A 22 D 19
B 25 E 23
C 25 F 21
I would have liked to know what the hearing scores of both groups was before eating.
To determine whether the results support the researcher's theory that people can hear better after eating a large meal, we can conduct a t-test for independent samples.
(a) Steps of Hypothesis Testing:
Step 1: State the null and alternative hypotheses.
Null Hypothesis (H0): There is no difference in hearing ability between individuals who ate a large meal and those who ate a small meal.
Alternative Hypothesis (Ha): Individuals who ate a large meal have better hearing ability compared to those who ate a small meal.
Step 2: Set the significance level.
The significance level (α) is given as .05.
Step 3: Determine the test statistic.
We will use a t-test for independent samples to analyze the data. The test statistic is calculated as the difference between the means divided by the standard error of the difference.
Step 4: Calculate the p-value.
Using the test statistic, we can find the p-value associated with it. The p-value represents the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.
Step 5: Make a decision.
Compare the p-value to the significance level. If the p-value is smaller than the significance level, we reject the null hypothesis in favor of the alternative hypothesis. Otherwise, we fail to reject the null hypothesis.
(b) Sketch the distributions involved:
To sketch the distributions involved, we need to draw histograms or boxplots to illustrate the hearing ability scores for both the big meal group and the small meal group. This will help visualize the data and assess whether there are any notable differences between the two groups.
After conducting the analysis and calculations, we can determine whether the results support the researcher's theory.