Complete the following questions by the due date. The total possible points to b

Question

Complete the following questions by the due date. The total possible points to be earned is 80. The final is worth 30% of your overall final course grade. A plot 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 860mug/dL, conduct a hypothesis test to determine if those who take supplements have significantly different levels of serum alpha tocopherol with alpha = 5% and the sample standard deviation is 472.57 mug/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. plusminus 1.7613 c. plusminus 1.645 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 plot 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 477.577. What sample size is needed to ensure adequate power based on question 7 if it suspected there will be 15% attrition?

Explanation / Answer

1. Here the appropriate test will be one sample t-test. So option( a) is the correct choice.

2. The alternative hypothesis is those who take vitamin E supplements have significantly different alpha-tocopherol levels.

So option (b) is the correct choice.

3. The critical values are upper 95% point and lower 5% point of t-distribution with 14 d.f . Those values are 2.1448 and -2.1448. So option(d) is the correct choice.

4. The sample mean is 1190. So option (a) is the correct choice.

5. The test statistic value = 2.99.

6. Since the test-statistic is greater than critical values, so we reject H0.

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