Question

Basic concepts. We design a study to evaluate a new medical treat- ment. We wish to show that the probability that a given patient will respond to the treatment is greater than 40%. We will treat 45 pa- tients. Let X be the number of patients who respond. Let p be the proportion of patients who respond. We will compute a Z score based on İ. If Z 1.8257, I will decide the response rate is > 0.40. If Z < 1.8257, I will not decide the response rate is0.40. If the re- sponse rate is 0.40, then P(Z > 1.8257)-0.03. If the response rate is 0.00, P(Z > 1.8257) 0.82. When I run the trial, I observe 22 response which yields a z value of 1.2172. I compute p to be 0.49. The probability that Z will be > 1.2172 is 0.11 if the probability of response is 40% and 0.94 if the probability of response is 60%. In the following questions, give the answer of the correct response (a, b,c,ord). 1. What is the null hypothesis we are testing? - a) Ho :p 0.4 -b) Ho P>0.4 c) Ho :p<0.4 2. What is the alternate hypothesis? -а) H. : p 0.4 - b) Ha :p> 0.4 -c) Ha :p<0.4 3. What test statistic are we using? a) p - b) x - c) Z - d) t 4. What is the rejection region for our test? -a) 0.40 - b) Z21.8257 - c) Z <1.8257 d) Z-1.8257

Answer 1

From given information,

1) The null hypothesis is,

a) H₀ : p = 0.40

2) The alternative hypothesis is,

b) H₀ : p > 0.40

3) The test statistic used is,

c) Z

4) The rejection region for this test is,

b) $Z \geq 1.8257$