Question

A weight loss program claims that program participants have a mean weight loss of at least 10 pounds after 1 month. You work for a medical association and are asked to test this claim. A random sample of 30 program participants and their weight losses (in pounds) after 1 month is listed in the table below. Assume the population standard deviation is 3. At α = 0.01, is there enough evidence to reject the program's claim?

Samples: 4.7, 6.0, 7.2, 8.3, 9.2, 10.1, 14.0, 11.7, 12.8, 10.8, 11.0, 7.2, 8.0, 4.7, 11.8, 10.7, 6.1, 8.8, 7.7, 8.5, 9.5, 10.2, 5.6, 6.9, 7.9, 8.6, 10.5, 9.6, 5.7, 9.6

For the problem, please approach your calculation from Classical Approach, P-Value Approach and C.I. Approach (if possible), and write all of your conclusions in context to the specific problem. Thanks.

Answer 1

H₀ : Here mean weight loss is greater than 10 pounds after 1 month. >= 10 pounds

H_a : The mean weight loss is less than 10 pounds after 1 month. <  10 pounds

Here population standard deviation = = 3 pounds

sample size = n = 30

sample mean = = 8.78 gms

standard error of sample mean = se₀ = /sqrt(n) = 3/sqrt(30) = 0.5477

Test statistic

Z = ( - _H)/se₀ = (8.78 - 10)/0.5477 = -2.2274

p - value = Pr(z < -2.2274)

using excel normsdist function

p - value = NORMSDIST(-2.2274) = 0.01296 > 0.01

so we fail to  reject the claim.

Now using confidence interval method.

we will use 98% confidence interval as we have significance level = 0.01

critica value for 98% confidence level = 2.326

98% confidence interval = +- Z_98% se = 8.78 +- 2.326 * 0.5477 = (7.506 pounds, 10.054 pounds)

as the value consist of 10 pounds so we failed to reject the null hypothrsis here.

So as we can see that we fail to reject the null hypothesis herre in both the case so we conclude here that weight loss program claim is correct that program participants have a mean weight loss of at least 10 pounds after 1 month