Question

5. A weight loss program advertises that participants in this program lose, on the average, 15 pounds. A random sample of 19 participants yielded a sample mean (X) of 14.73, and a sample standard deviation (%) of 2.2. Is this sufficient statistical evidence that would make us not believe the claim offered by the program? Clearly state the null and alternate hypotheses, along with any signiicant statıstical evidence used to reach your decision.

Answer 1

H₀: $\mu$ = 15

H₁ : $\mu$ < 15

The test statistic t = ( $\bar x - \mu$ )/(s/sqrt(n))

                            = (14.73 - 15)/(2.2/sqrt(19))

                            = -0.53

At alpha = 0.05, the critical value is t_{0.05, 18} = -1.734

As the test statistic value is not less than the critical value (-0.53 > -1.734), so the null hypothesis is not rejected.

So at 5% significance level there is not sufficient evidence to support the claim offered by the program that the participants in this program lose weight from the average 15 pounds.