Question

Consider the following hypotheses.

Ho p<0.16

H, p>0.16

Given that p=0.2 n = 140 and a=005, answer the following questions

a. What conclusion should be drawn?

b. Determine the p-value for this test.

a. Determine the critical value(s) of the test statistic

Answer 1

Solution :

The null and alternative hypotheses are as follows:

To test the hypothesis we shall use z-test for single proportion. The test statistic is given as follows:

Where, p is sample proportion, P is hypothesized value of population proportion, Q = 1 - P and n is sample size.

p = 0.2, P = 0.16, Q = 1 - 0.16 = 0.84 and n = 140

The value of the test statistic is 1.29099.

Since, our test is right-tailed test, therefore we shall obtain right-tailed p-value for the test statistic, which is given as follows:

p-value = P(Z > value of the test statistic)

p-value = P(Z > 1.29099)

p-value = 0.09835

a) significance level = 0.05

(0.05 < 0.09835)

Since, p-value is greater than the significance level of 0.05, therefore we shall be fail to reject H​​​​​​0 at 0.05 significance level.

b) The p-value is given as follows:

p-value = P(Z > value of the test statistic)

p-value = P(Z > 1.29099)

p-value = 0.09835

c) The critical value of the test statistic at 0.05 significance level is given as follows:

Critical value = Z(0.05) = 1.645

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