Suppose a new weight loss program was sponsored by the local health and fitness club in a small town. The program claims to make people lose more than five pounds in a month. Twelve participants were selected and their weights were recorded. After a month of the program their weights were recorded again. It was found that many participants lost some weight. But there was variation. Some lost more and some lost less, and some did not lose any pound at all. The measurements were as follows:
Obs Before After
1 ........... 217 202.5
2 ........... 188 178
3 ........... 225 210
4 ........... 168 157
5 ........... 178 169
6 ........... 182 180
7 ........... 174.5 163.5
8 ........... 161.5 153
9 ........... 177.5 178
10 ......... 358.5 336
11 ......... 181 174
12 ......... 210 197.5
Test the claim of the program sponsors at reasonable levels of significance.
We can use calculator to find the paired differences then find its mean and standard deviation, then standard error of the sample mean difference, and then perform the t-test using t- table.
I will give the computer result here. Show result using calculator, formula and t-table.
Hypothesis Test: Paired Observations
5.0000 hypothesized value
201.7500 mean before
191.5417 mean after
10.2083 mean difference (before - after)
5.9979 std. dev.
1.7315 std. error
12 n
11 df
3.01 t
.0060 p-value (one-tailed, upper)
The p-value shows that the Null hypothesis that the weight loss is less than or equal to five pounds is strongly rejected even at 1% significance level. Therefore, the claim of this hypothetical weight loss programs has strong support from this sample.