A pilot study to evaluate the serum alpha tocopherol levels (serum vitamin E) wa

Question

A pilot study to evaluate the serum alpha tocopherol levels (serum vitamin E) was conducted to evaluate the toxicity among 14 people who regularly take vitamin-E supplements. The vitamin E levels for the 15 participants are listed below. If the level of alpha tocopherol in the general population 860 mu g/dL, conduct a hypothesis test to determine if those who take supplements have significantly different levels of serum alpha tocopherol with alpha a 5% and the sample standard deviation is 472.57 mu g/dL. 690 2010 1350 780 1505 1235 810 1990 1105 655 1010 1570 980 1005 1150 What hypothesis test is appropriate to answer this research question? a. One-sample t test b. One sample Z Test c. Matched t Test d. Chi-Square test for association/independence What is the alternative hypothesis? a. There is no significant difference in serum alpha tocopherol levels. b. Those who take vitamin-E supplements have significantly different alpha tocopherol levels. c. Those who take vitamin-E supplements have significantly greater alpha tocopherol levels. d. Those who take vitamin-E supplements have significantly lower alpha tocopherol levels. What is the critical value? a. plusminus 1.96 b. +1.7613 c. +1.545 d. plusminus 2.1448 What is the sample mean? a. 1190 b. 1275 c. 860 d. 472.57 what is the test statistic rounding to two decimal places? a. 3.12 b. 2.70 c. 2.41 d. 1.59 True or False: Fail to reject H_2 as the test statistic does not fall within the rejection region. Suppose the investigator of the pilot study wants to expand to a larger study to make sure 80% power is achieved. What sample size is needed to detect a difference in means of 75 given the standard deviation of 472.57? What sample size is needed to ensure adequate power based on question 7 If it is suspected there will be 15% attrition?

Explanation / Answer

1) We use one sample t test here.

2) Alternative hypothesis is Those who take vitamin E suplements have significantly different alfa tocopherol level.

Note here that we are just testing its similar level or different level .

That is we are not guesing about greater or lower level.

3) For 15 sample t14value at 0.05 significance level is 1.7613

4) From given data sample mean is sum of all values divided by total observations (15)

sample mean is 1190.

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