Suppose you are interested in investigating the factors that affect the prevalen

Question

Suppose you are interested in investigating the factors that affect the prevalence of tuberculosis among intravenous drug users. In a group of 100 individuals who admit to sharing needles, 15 had a positive tuberculin skin test result. The state department of health recently released that the state population proportion of positive tuberculin skin tests is 12%. Test the hypothesis that the sample of intravenous drug users have a higher proportion of positive TB skin tests than the general population with alpha 0.05. Round all intermediate calculations to 4 decimal places. 11. What are the null and alternative hypotheses? (2 pts) 12. What is the critical value? Round to 4 decimal points. (2 pts) a. Z#-1.96 b. Z 1.96 c. Z-1.645 d. 2 -1.645 13. What is the test statistic? Round final answer to 2 decimal points. (3 pts) a. 28.41 b. 0.92 C.9.23 d. -10.37 14. Is there a significant difference in the proportion of positive tuberculin skin tests among the intravenous drug users and the general population? (2 pts) Reject Ho in favor of Ha as the test statistic is less than the critical value. b. a. Reject Ho in favor of Hs as the test statistic is greater than the critical value. c. Fail to reject Ho in favor of Ha as the test statistic is less than the critical value. d. Fail to reject Ho in favor of Hs as the test statistic is greoter than the critical value 15. What is the p-value of the test statistic calculated in question 137 Round to 4 decimal places. (2 pts) a. 0.1788 b. 0.8212 c. 0.9999 d. 0.0001

Explanation / Answer

Question 11

Correct null and alternative hypotheses are given as below:

d. H­0: p = p0: Ha: p > p0

(test ask for higher proportion)

Question 12

We are given = 0.05, n = 100, x = 15

So, by using z-table or excel, critical value is given as below:

c. Z = 1.6449

Question 13

We are given = 0.05, n = 100, x = 15

P = x/n = 15/100 = 0.15

H­0: p = 0.12: Ha: p > 0.12

q = 1 – p = 1 – 0.12 = 0.88

Test statistic = Z = (P – p) / sqrt(p*q/n)

Z = (0.15 – 0.12)/sqrt(0.12*0.88/100)

Z = 0.03/ 0.032496

Z = 0.923191

Correct Answer: b. 0.92

Question 14

Correct Answer:

c. Fail to reject H0 in favour of Ha, as the test statistic is less than the critical value.

(we reject null hypothesis when test statistic value is less than critical value.)

Question 15

Correct answer: a. 0.1788

(by using z-table or excel)

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