1. What hypothesis test is appropriate to answer this research question? 2. What

Question

1. What hypothesis test is appropriate to answer this research question?

2. What is the alternative hypothesis?

3. What is the critical value?

4. What is the sample mean?

5. What is the test statistic rounding to two decimal places?

6. True or False: Fail to reject H0 as the test statistic does not fall within the rejection region.

7. 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?

8. What sample size is needed to ensure adequate power based on question 7 if it is suspected there will be 15% attrition?

s/blackboardfexecute/content/file?cmdaview&content; 607g47 1&course; ids 11330.1 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 ug/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 ug/dL. 690 2010 1350 780 1505 1235 810 1990 1105 655 1010 1570 980 1005 1150 1. What hypothesis test is appropriate to answer this research question? a. One-sample t test b. One-sample z Test Matched t Test d. Chi-Square test for association/independence 2. 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. 3. What is the critical value? a. t1.96 b. +1.7613 +1.645 d. 12.1448

Explanation / Answer

Answer 1:

Option a is correct.

One sample t-test is appropriate to answer this question because sample size is less than 30 and population standard deviation is unknown.

Answer 2:

Option b is correct.

Alternative Hypothesis (Ha): µ 860, those who take Vitamin E supplements have significantly different alpha tocopherol levels.

Answer 3:

Option d is correct.

We have a = 0.05 and n = 15

Degrees of freedom, df = n -1 = 15 -1 = 14

Using t-tables, the critical value is

t (0.05/2, 14) = t (0.025, 14) = ±2.1448

Answer 4:

Sample mean, X-bar = X/n

Sample mean, X-bar = (690+2010+1350+780+1505+1235+810+1990+1105+655+1010+1570+980+1005+1150)/15

Sample mean, X-bar = 17845/15

Sample mean, X-bar = 1189.667

Answer 5:

Test Statistics

t = (X-bar - µ)/ (s/n)

t = (1189.667 – 860)/ (472.57/15)

t = 2.70

Answer 6:

False

Since test statistics lie outside the critical value, we reject Ho.

Answer 7:

The sample size is given by:-

N = [Z (1 – ) + Z (1 - a/2)]^2 ^2/(µ0 - µ1)^2

N = [Z (1 – 0.80) + Z (1 – 0.05/2)]^2 (472.57)^2/(75)^2

N = [0.84 + 1.96]^2 (472.57)^2/75^2

N = 311.26

N = 312

Answer 8:

Since there is 15% attrition, the sample size would be 312 x (1 + 15%) = 358.8 ~ 359.

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