In a study, four individuals with varying levels of cholesterol went on a special crash diet. Some would say that there is a connection between high cholesterol foods and high blood cholesterol levels, but this theory has yet to be proven. The sample of four subjects have displayed their total blood cholesterol levels before and after the diet as:
| Participant |
| ----------- |
| Collin |
| Ignacio |
| Joseph |
| Paulina |
| Before |
| ------ |
| 279 |
| 270 |
| 290 |
| 306 |
| After |
| ----- |
| 258 |
| 301 |
| 257 |
| 298 |
Using a $2 \%$ level of significance, was there a significant decrease in cholesterol level in the blood on average? Assume that cholesterol level in the blood is normally distributed.
1. Complete the populations, null and researcher's hypothesis
Population 1:
The set of all $\square$ Select an answer in the blood $\square$ Select an answer
Population 2:
The set of all $\square$ Select an answer in the blood $\square$ Select an answer
$\begin{array}{l}
H_0: ? V \square ? \square \\
H_{r}: ? V \square ? \square
\end{array}$
2. Which test would you use to verify the requirements? $\square$ $n \geq 30$ or $X$ is normally distributed ${ }^{\circ}$
Has the requirements of the test met? $\square$ Yes $\square$ of
What is the sampling distribution? $\square$ Student t-distribution
3. Determine the cutoff score (critical value) for significance. $\square$
4. Fill in the blank for the necessary statistics to test the claim. Use the to help you round your answers.
n =$\square \overline{ x }_{d}=\square \text { and } s _{d}=\square$
5. Determine the standardized sample score (from the sample taken) Round your answer to four decimal places. $\square$
6. Determine the $p$-value from the standardized sample score. Round your answer to four decimal places. $\square$
7. Make your decision to reject or fail to reject the null hypothesis.
Select an answer $V$
Answer (2)
Fail to reject the null hypothesis.
Examples
In medical research, determining the effectiveness of a new diet or drug often involves comparing measurements before and after the intervention. This type of hypothesis testing helps researchers decide whether the observed changes are statistically significant or simply due to random chance. For example, a study might investigate if a new medication lowers blood pressure significantly compared to a placebo. The same method can be applied in educational settings to assess the impact of a new teaching method on student performance.
The cholesterol levels of four individuals were analyzed before and after a crash diet. Using a t-test, the results indicated that there was not enough evidence to conclude a significant decrease in cholesterol levels after the diet, leading to a failure to reject the null hypothesis. Thus, we cannot definitively say the diet decreased blood cholesterol levels significantly.
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