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.)

(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

Step-by-step 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