Question

A cholesterol level over 200 is considered high. The manufacturers of a certain brand of cereal are interested in whether eating their cereal for breakfast daily will result in a decrease in cholesterol levels for people with high cholesterol. They randomly select ten people with high cholesterol to participate in the study. Each subject eats the cereal every morning for a month. The cholesterol levels of each subject are measured before and after the study. The results are shown in the table below.

Person 1 2 3 4 5 6 7 8 9 10

Cholesterol before study 210 245 230 215 220 279 240 238 225 247

Cholesterol after study 200 220 235 205 195 239 218 219 226 233

6. Conduct an hypothesis test at the 2.5% significance level to determine if the there was a significant decrease in average cholesterol for the participants in this study (assume cholesterol levels follow a normal distribution so the normality requirement is met). What are your null and alternative hypothesis?

7. You want to conduct an hypothesis test at the 2.5% significance level to determine if the there was a significant decrease in cholesterol for the participants in this study (assume cholesterol levels follow a normal distribution so the normality requirement is met). What is the value of the test statistic to one decimal place?

8. For your hypothesis test from the last question, what is your conclusion? (Note: you may assume that the absolute value of the critical value is approximately 2 for the calculation in this part)

9. This study did not meet the requirements of an experiment, so it was simply an observational study. Which requirements of an experiment were not met?

Answer 1

Let us denote the difference

d = Cholesterol before study - Cholesterol after study