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).
The null hypothesis $H_0:\mu_d = 0$ (no difference in cholesterol levels on average).
The alternative hypothesis $H_1:\mu_d> 0$ (cholesterol levels are lower on average after the diet, so we are interested in one - sided increase in the difference (Before - After)).

Step2: Determine the type of test

Since we are only interested in whether the mean difference is positive (cholesterol levels are lower on average after the diet), this is a one - tailed test.

Answer:

Null hypothesis: $H_0:\mu_d = 0$; Alternative hypothesis: $H_1:\mu_d>0$; One - tailed test.