Question

Consider the following hypotheses.

Upper H 0​: p ≤ 0.11
Upper H 1​: p ≠ 0.11
Given that p = 0.16​, n =150​, and α = 0.01​, answer the following questions.
(a) What conclusion should be​ drawn?
(b) Determine the​ p-value for this test.
(c) Determine the critical​ value(s) of the test statistic. zₐ =1.96 ​(Use a comma to separate answers as needed. Round to two decimal places as​ needed.)

Answer 1

(a) There is sufficient evidence to conclude that the population proportion equals 0.11.

(b) p-value is 0.0548

(c) Critical values are -2.58, 2.58

Explanation:

(a) Conclusion:

Fail to reject H0 because the p-value 0.0548 is greater than the significance level 0.01.

(b) The test is a two-tailed test because the alternate hypothesis is expressed using not equal to.

Test statistic (z) = (p' - p) ÷ sqrt[p(1-p) ÷ n]

p' is sample proportion = 0.16

p is population proportion = 0.11

n is sample size = 150

z = (0.16 - 0.11) ÷ sqrt[0.11(1-0.11) ÷ 150] = 0.05 ÷ 0.026 = 1.92

Cumulative area of the test statistic is 0.9726

p-value for a two-tailed test = 2(1 - 0.9726) = 2(0.0274) = 0.0548

(c) The critical values of the test statistic are -2.58, 2.58