Question

In Example 1.4 we looked to see whether the competent-face method could be used to predict the results of Senate races. We found this method worked in 23 out of 32 races. When testing to see if the probability of this method working is more than 0.50,we obtained a null distribution similar to that shown. Probability of heads: 0.5 Number of tosses: 32 Number of repetitions: 1000 180 Mean=0.501 SD = 0.090 120 60 lu 8.19 0.28 0.38 0.47 0.56 0.66 0.75

Answer both questions

Answer 1

It is given the sample size is 32. It is given that the competent-face method worked in 23 out of 32 races. The test was performed to see if the probability of this method working is more than 0.50. The null hypothesis is H :p 50.5 The alternative hypothesis is He:p> 0.5 The data is given as follows: Probability of heads: 0.5 Number of tosses: 32 Number of repetitions: 1000 It is given that a 2SD 95% confidence interval for the probability that the competent-face method will work was CI = 0.72 2(0.09) = (0.54,0.9) Since the confidence interval does not contain 0.5, the null hypothesis is rejected. Thus, it can be concluded that the probability that the competent face method will work is greater than 50% Therefore, the correct answer is TRUE. A theory-based approach should not be used to compute the confidence interval for this data because the sample size is smaller than 20% of the total population.

Answer 2

Lolor 1) The 95% cf for proporth is 4 p & L412 vn pq $=2-23 20.12 n = 32 P=0.50, q=0.50 1.96 2412=

0.72 1 2x10.5xos 32 ..012 + 2*10.09) (0.54 0.go) This is mie which is greater than 50% 2 The sample size is smaller than 20% of the total population,