suppose a random sample of 200 observations from a binomial population has produ
ID: 3240850 • Letter: S
Question
suppose a random sample of 200 observations from a binomial population has produced p-o33 and we wish to test Ho p o40 against the alematve Hip 040 Complete parts a through d a. calculate the value ofthe zstatistic for tis test. z. (Round to two decimal places as needed. b. Note that the numerator of the z-statisticis the same as if n 200, p 0.14. and we wish test Ho p 021 againstthe alternative Ha: p 021. smaller than that calculated for the revised test? Select the correct choice below and boxes to complete your choice. fill in the answer Considering this, why is the absolute value of z for the original test (Round to four decimal places as needed.) OA The denominator for the original test is .compared to for the revised test sinoe the denominator for the original testis smaller, the absolute value ofzis smaller. OB. The denominator for the original test is for the revised test. Since the denominator for the original testis larger, the absolute value of zis smaler. c. Complete the test using a 0.01 and interpret the result. what is the rejecson region? Select the correct choice below and ful in the answer boxes) to complete your choice. (Round to two decimal places as needed) o B. What is the conclusion of the test? the null hypothesis because the test statistic in the rejection region. Therefore, there is evidence at the 001 level of significance to indicatethat the population proportion is less than 040.Explanation / Answer
a. The z test statistic, z=(phat-p)/sqrt[{p(1-p)}/n], where, phat is sample proportion, p is population proportion, n is sample size.
=(0.33-0.40)/sqrt[{(1-0.40)0.40}/200]
=-2.02 (ans)
b. The denominator for original test is 0.0346[sqrt{(1-0.40)0.40}/200]. compared to 0.0288 [sqrt{(1-0.21)0.21}/200]. Ans> B.
c. The original test is left tailed. Given, alpha=0.01. Therefore, the rejection region is: z<-2.33. Ans>C.
Fail to reject [the test statistics, z=-2.02 do not fall in critical region, z<=-2.33] insuffient evidence at the 0.01 level of significance to indicate that population proportion is less than 0.40.
d. The p value is: 0.0217.
The p value means the probability of finding an observed or more extreme result when the null hypothesis is true. Thus, Option B is correct.
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