Question

A brochure inviting subscriptions for a new diet program states that the participants are expected to lose at least 10 kg in five weeks. Suppose that, from the data of the five-week weight losses of 16 participants, the sample mean and standard deviation are found to be 8.68 and 2.5 kg, respectively. Assume that the weight loss is normally distributed. At 5% significance level, could the statement in the brochure be supported on the basis of these findings? (Write down the hypotheses, calculate the test statistic, the P-value and make a conclusion.).

Answer 1

we write the null and alternate hypothesis as

the test statistic is given by ,

we have ,

we get test statistic for as

we get p value from t distribution table since n<30 , with degrees of freedom n-1=15

since p value 0.0259 is less than , we reject null hypothesis , so there is sufficient evidence that the participants would loss atleast 10 kg in five weeks with the new diet program