Question

(Can you give me an example of data and calculations from this example below?) Hypothesis testing for the mean and P-values, left tailed and right tailed, z test... An example to use could be if a weight loss product, which would be a list of meal plans, works. You could gather 100 people that are subscribers and users of this program and calculate the amount of weight they are losing within a span of 6 months. The claim could be that the program would have you lose up to 50 pounds in the 6 month time frame.

Answer 1

n =sample size =100 people.

Let X1 =weights before 6 months (before using the product).

X2 =weights after 6 months (after using the product).

Let the mean of differences between after weight and before weight is: = -70 pounds.

Let Standard deviation of the differences is: =20 pounds. (where d =X2 - X1).

Paired samples t-test:

Null Hypothesis (H0):

The mean weight loss after 6 months is not significantly greater than from 50 pounds. ​​​​​​

Alternative Hypothesis (H1):

The mean weight loss after 6 months is more than 50 pounds. (left-tailed test).

Test statistic:

t = = -70/(20/​​​​​​) = -35

​​​​​​P-value:

Let the significance level, =0.05

Degrees of freedom, df =n - 1 =99

The P-value for t = - 35 at df =99 and =0.05 for one-tailed test is: P-value < 0.00001

Conclusion:

Since, P-value < (0.05), there is a strong evidence to reject the null hypothesis in favor of the alternative hypothesis. Thus, the mean weight loss after 6 months (after using the product) is more than 50 pounds.