ANOVA Statistic Assingment Help With Solution

Complete the following questions and submit your answers via Blackboard by the due date. The total
possible points earned is 38 points. Round all calculated values to 4 decimal points if necessary.
Use the following information to answer questions 1 – 10.

With all the fad diets advertised on TV, a researcher wanted to know if there was a significant differencein 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
5 12 3
2 10 2
3 8 1
4 4 0

1. What are the null and alternative hypotheses?
a. H0: 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. H0: 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. H0: 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. H0: 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?
a. 2
b. 3
c. 11
d. 12

3. What are the dfwithin?
a. 9
b. 10
c. 11
d. 12

4. What is the critical value? (Round to 4 decimal places)
a. 3.8853
b. 3.9823
c. 4.2565
d. 3.5874
Complete the table below.
SS df MS F
Between
Within 45
Total 149

5. What is SSbetween?
a. 45
b. 104
c. 149
d. 194

6. What is MSbetween?
a. 5
b. 34.667
c. 52
d. 74.5

7. What is MSwithin?
a. 22.5
b. 34.667
c. 52
d. 5

8. What is the F test statistic?
a. 10.4
b. 0.096
c. 4.2565
d. 1.541

9. What is the conclusion based on your test statistic?
a. 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.
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. 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.

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Use the following information to answer questions 11 – 18.

Suppose researchers do an epidemiologic investigation of people entering a sexually transmitted disease
clinic. Given the observed table below and α = 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

10. 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

11. What is the critical value?
a. 2.71
b. 3.84
c. 5.02
d. 6.63

12. What is the expected value of those with a present diagnosis of gonorrhea having a previous
episode of urethritis?
a. 81.69
b. 91.69
c. 118.31
d. 63.31

13. What is the expected value of those with a present diagnosis of gonorrhea not having a previous
episode of urethritis?
a. 81.69
b. 91.69
c. 118.31
d. 63.31

14. What is the expected value of those with a present diagnosis of nongonococcal urethritis having
a previous episode of urethritis?
a. 81.69
b. 91.69
c. 118.31
d. 63.31

15. What is the expected value of those with a present diagnosis of nongonococcal urethritis not
having a previous episode of urethritis?
a. 81.69
b. 91.69
c. 118.31
d. 63.31

16. What is the test statistic?
a. 45.8
b. 82.4
c. 38.5
d. 105.6

17. Is there is an association between present diagnosis and prior episodes of urethritis?
a. Reject H0 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 H0 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 H0 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 H0 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.

18. What is the sample size needed for the confidence interval estimate? Round up to the next integer.
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 α =0.05, 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.

19. What is the sample size needed to be able to conduct their hypothesis test? Round up to the next integer.

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