With all the fad diets advertised on TV, a researcher wanted to know if there was a significant difference in weight loss depending on which new fad diet you were on. Over the course of 2 weeks, a total of 15 male volunteers who weighed the same and had similar lifestyles were broken up into 3 groups: Diet 1, Diet 2, and Diet 3. Conduct an ANOVA on the following table with alpha = 0.5 to determine if at least one of the diets has significantly different weight loss compared to the other two.
Diet 1 Diet 2 Diet 3
3 5 12
2 2 10
1 3 8
0 4 4
4 1 1
1. What are the null and alternative hypothe:
a. Ho: Mean weight loss from Diet 1 = mean weight loss from Diet 2 = mean weight loss from Diet 3
HA: Mean weight loss from Diet 1 > mean weight loss from Diet 2 > mean weight loss from Diet 3
b. Ho: Mean weight loss from Diet 1 = mean weight loss from Diet 2 = mean weight loss from Diet 3
HA: At least one mean weight loss is significantly different
c. Ho: At least one mean weight loss is significantly different
HA: Mean weight loss from Diet 1 > mean weight loss from Diet 2 > mean weight loss from Diet 3
d. Ho: Mean weight loss from Diet 1 = mean weight loss from Diet 2 = mean weight loss from Diet 3
HA: Mean weight loss from Diet 1 < mean weight loss from Diet 2 < mean weight loss from Diet 3
2. What are the dfbetween?
3. What are the dfwithin?
4. What is the critical value? (Round to 4 decimal places)
Complete the table below.
SS df MS F
Between
Within
Total
5. What is SSbetween?
6. What is SSwithin?
7. What is MSSbetween?
8. What is MSwithin? (Round to 2 decimal places)
9. What is the F test statistic? (Round to 1 decimal place)
10. What is the conclusion based on your test statistic?
a. Reject the null hypothesis because the test statistic did fall in the rejection region. There is sufficient evidence that there is a significant difference in the mean weight loss for at least one of the diets.
b. Fail to reject the null hypothesis because the test statistic did fall in the rejection region. There is not sufficient evidence that there is a significant difference in the mean weight loss for at least one of the diets.
c. Reject the null hypothesis because the test statistic did not fall in the rejection region. There is sufficient evidence that there is a significant difference in the mean weight loss for at least one of the diets.
d. Fail to reject the null hypothesis because the test statistic did not fall in the rejection region. There is not sufficient evidence that there is a significant difference in the mean weight loss for at least one of the diets.
Suppose researchers do an epidemiologic investigation of people entering a sexually transmitted disease clinic. Given the observed table below and a = 0.05, conduct a chi-square test for association to determine if there is an association between present diagnosis and prior episodes of urethritis.
Previous Episodes of Urethritis
Yes No
Present Diagnosis Gonorrhea 160 40
Nongonococcal Urethritis 50 105
11. What is the alternative hypothesis?
a. There is no association between present diagnosis and prior episodes of urethritis
b. There is an association between present diagnosis and prior episodes of urethritis
c. The presence of diagnosis is greater for those with a prior episodes of urethritis
d. The presence of diagnosis is less for those with a prior episodes of urethritis
12. What is the critical value?
13. What is the expected value of those with a present diagnosis of gonorrhea having a previous episode of urethritis? Round to the first decimal place.
14. What is the expected value of those with a present diagnosis of gonorrhea not having a previous episode of urethritis? Round to the first decimal place.
15. What is the expected value of those with a present diagnosis of nongonococcal urethritis having a previous episode of urethritis? Round to the first decimal place.
16. What is the expected value of those with a present diagnosis of nongonococcal urethritis not having a previous episode of urethritis? Round to the first decimal place.
17. What is the test statistic? Round to the first decimal place.
18. Is there is an association between present diagnosis and prior episodes of urethritis?
a. Reject Ho in favor of HA because the test statistic falls within the rejection region. There is sufficient evidence that there is an association between present diagnosis and prior episodes of urethritis.
b. Fail to reject Ho in favor of HA because the test statistic does not fall within the rejection region. There is not sufficient evidence that there is an association between present diagnosis and prior episodes of urethritis.
c. Reject Ho in favor of HA because the test statistic did not within the rejection region. There is sufficient evidence that there is an association between present diagnosis and prior episodes of urethritis.
d. Fail to reject Ho in favor of HA because the test statistic falls within the rejection region. There is not sufficient evidence that there is an association between present diagnosis and prior episodes of urethritis.
We are interested in studying the BMI of group of middle-aged men at risk for developing diabetes mellitus. The standard deviation of the BMI for the population is 2.65 kg/m2. Determine the number of subjects needed to estimate the true mean BMI within 0.75 units using a 95% confidence interval.
19. What sample size equation will be needed?
a. dichotomous, one group sample size for confidence interval estimate
b. continuous, one group sample size for hypothesis test
c. continuous, one group sample size for confidence interval estimate
d. dichotomous, one group sample size for hypothesis test
20. What is the sample size needed?
A study is being planned to estimate the proportion of students aged 16 to 20 who drive under the influence of drugs or alcohol. Determine the number of subjects needed to estimate 6% of the true proportion with 95% confidence.
21. What sample size equation will be needed?
a. dichotomous, one group sample size for confidence interval estimate
b. continuous, one group sample size for hypothesis test
c. continuous, one group sample size for confidence interval estimate
d. dichotomous, one group sample size for hypothesis test
22. What is the sample size needed?
An investigator wants to evaluate the efficacy of an acupuncture treatment for reducing pain in patients with chronic migraine headaches. The plan is to enroll patients who suffer from migraine headaches. Each will be asked to rate the severity of the pain they experience with their next migraine before any treatment is administered. Pain will be recorded on a scale of 1-100 with higher scores indicative of more severe pain. Each patient will then undergo the acupuncture treatment. On their next migraine (post-treatment), each patient will again be asked to rate the severity of the pain. The difference in pain will be computed for each patient. A two sided test of hypothesis will be conducted, at a 4.05, to assess whether there is a statistically significant difference in pain scores before and after treatment. How many patients should be involved in the study to ensure that the test has 80% power to detect a difference of 12 units on the pain scale? Assume that the standard deviation in the difference scores is approximately 20 units.
23. What sample size equation will be needed?
a. continuous, two independent groups sample size for hypothesis test
b. continuous, matched groups sample size for hypothesis test
c. continuous, independent groups sample size for confidence interval estimate
d. continuous, matched groups sample size for confidence interval estimate
24. What is the sample size needed?
Suppose the investigator expects 10% of the original patients will be lost to the study.
25. How many samples does the investigator now need to account for 10% attrition?