1. A research study examined the effect of low-carbohydrate diet on cholesterol levels. Participants' cholesterol levels are measured before starting the diet program and then again after 6 months on the program. Sample data are provided below. Conduct an appropriate statistical test to examine if average cholesterol level is different between the groups. Assume all assumptions for this test are met. Significance level is set at 0.05 for a two-tail test.

Participant ID	1	2	3	4	5	6
Baseline	210	230	190	215	260	200
At 6 months	215	240	190	200	280	210

1. Provide null and alternative hypotheses
2. Provide formulas and all intermediate steps involved in the calculation of the test statistic
3. Test statistic value
4. P-value
5. Full conclusion and concluding statement for the research question.

Question 2:

Previous studies have estimated the mean systolic blood pressure among youth adults to be 110 mmHg, with a standard deviation of 2 mmHg.

a. How many participants will the researcher need to recruit if she expects the mean blood pressure to be higher by 1 mmHg. The rate of type I error is 5% and type II error is 10% for a two-tail test. Provide formula and all steps involved in the calculation

b. Now, if the researcher managed to use the rate of type I error at 5% and type II error at 20% for a two-tail test, how many participants will the researcher need to recruit? (You do not need to re-write the code or show your calculations again. Simply provide the final sample size).

c. If 80% is the minimum amount of study power required to detect a difference, do you think that this researcher has enough study power if she enrolls 25 people? (Circle one.)

Yes No