Question

A large company that produces a "fat-burner" pill claims an average loss of 20 pounds in the first month. A consumer advocacy group believes that this claim is actually just "hype" intended to sell more of the compound. The advocacy group would like to obtain statistical evidence about this issue and takes a random sample of 100 consumers who responded that they had purchased the pill but didn't know what the survey was about. They find that these 100 people lost an average of 18 pounds with a standard deviation of 7.5 pounds. What are the null and alternative hypothesis in this situation

Answer 1

Answer:

Based on the claim (the average loss is 20 pounds)  the system of hypothesis for this case are:

Null hypothesis $\mu = 20$

Alternative hypothesis: $\mu \neq 20$

Step-by-step explanation:

For thi case we want to test if the "fat-burner" pill present and average loss of 20 pounds in the first month.

And in order to test this hypothesis they have the following sample data:

$n = 100$ represent the sample size

$\bar X = 18$ the sample average fro the lost weight

$s = 7.5$

Based on the claim (the average loss is 20 pounds)  the system of hypothesis for this case are:

Null hypothesis $\mu = 20$

Alternative hypothesis: $\mu \neq 20$

And in order to test the hypothesis we can use the following statistic:

$t = \frac{\bar X -\mu}{\frac{s}{\sqrt{n}}}$