Question

a study was conducted to investigate how effective a new diet was in lowering cholesterol. results for the randomly selected subjects are shown in the table. the differences have a normal distribution. are the subjects cholesterol levels lower on average after the diet? test at the 5% level.
subject a b c d e f g h i
before 209 210 205 198 216 217 238 240 222
after 199 207 189 209 217 202 211 223 201
table 10.16
. write null and alternative hypotheses. is this one or two - tailed test?

Explanation:

Step1: Define the null and alternative hypotheses

Let \(\mu_d\) be the mean difference (Before - After).
\(H_0:\mu_d = 0\) (no difference, i.e., cholesterol levels are the same on average before and after the diet)
\(H_1:\mu_d> 0\) (cholesterol levels are lower on average after the diet, so difference (Before - After) is positive)

Step2: Determine the type of test

Since the alternative hypothesis \(H_1:\mu_d > 0\) has a direction (we are only interested in the case where the mean difference is positive), this is a one - tailed test.

Answer:

Null hypothesis \(H_0:\mu_d = 0\), alternative hypothesis \(H_1:\mu_d>0\). This is a one - tailed test.