Question

A group of six, obese adult women had their weights recorded both before and 9 months after having a diet treatment to help manage their weight. Observe the information presented in the table below:

The weights of six obese adult women both before and 9-months after having a diet treatment

Before Diet Treatment	After Diet Treatment
260	240
220	215
200	198
310	300
325	298
195	195

Test at α = 0.05 the hypothesis that for the group, there was a statistically significant average decrease in weight from before diet treatment to 9 months after. Hint: This is hypothesis testing for paired samples. Here, you will use a paired t test.

Answer 1

Consider the following table:

Subject	Before	After	Difference
A	260	240	20
B	220	215	5
C	200	198	2
D	310	300	10
E	325	298	27
F	195	195	0

For the score differences we have, mean is Dˉ=10.6667, the sample standard deviation is sD=10.7269, and the sample size is n=6. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: μD =0 Ha: μD >0 This corresponds to a Right-tailed test, for which a t-test for two paired samples be used. (2a) Critical Value Based on the information provided, the significance level is α=0.05, and the degree of freedom is n-1=6-1=5. Therefore the critical value for this Right-tailed test is tc​=2.015. This can be found by either using excel or the t distribution table. (2b) Rejection Region The rejection region for this Right-tailed test is t>2.015 (3)Test Statistics The t-statistic is computed as follows: (4) The p-value The p-value is the probability of obtaining sample results as extreme or more extreme than the sample results obtained, under the assumption that the null hypothesis is true. In this case, the p-value is 0.0295 (5) Decision about the null hypothesis (a) Using traditional method Since it is observed that t=2.4357<tc​=2.015, it is then concluded that the null hypothesis is rejected. (b) Using p-value method Using the P-value approach: The p-value is p=0.0295, and since p=0.0295≤0.05, it is concluded that the null hypothesis is rejected. (6) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ1​ is greater than μ2, at the 0.05 significance level.

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!