Answer: We can use a paired t-test to determine if there is a significant difference between the starting and ending cholesterol levels. The five-step process for hypothesis testing is as follows:
State the null and alternative hypotheses.
Null hypothesis: The mean difference between the starting and ending cholesterol levels is equal to zero.
Alternative hypothesis: The mean difference between the starting and ending cholesterol levels is less than zero (i.e., there was a significant reduction in cholesterol levels after the low-fat diet).
Determine the level of significance.
We will use a level of significance of 0.05.
Determine the critical value or p-value.
Since the alternative hypothesis is one-tailed, we will use a one-tailed t-test. With 9 degrees of freedom and a level of significance of 0.05, the critical t-value is -1.833.
Alternatively, we can use software or a t-table to find the p-value associated with the test statistic.
Since the test statistic (-0.90) is greater than the critical t-value (-1.833) and the p-value associated with the test statistic is greater than 0.05, we fail to reject the null hypothesis. This means that there is not sufficient evidence to conclude that the low-fat diet significantly reduced cholesterol levels.