Answer:
(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
