Question

The following hypotheses are given.

H₀ : π ≤ 0.81
H₁ : π > 0.81

A sample of 140 observations revealed that p = 0.92. At the 0.10 significance level, can the null hypothesis be rejected?

1. State the decision rule. (Round your answer to 2 decimal places.)

2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

3. What is your decision regarding the null hypothesis?

• Reject H₀.

• Do not reject H₀.

Answer 1

Given that a sample of n = 140 observations revealed that p = 0.92. At the 0.10 significance level.

Based on the hypothesis it will be a right-tailed test.

Rejetion region/ Decision rule:

Based on the type of hypothesis and the given significance level the critical value for the rejection region is calculated using the excel formula for normal distribution which is =NORM.S.INV(0.90) Thus the critical value is 1.28

So, reject Ho if Z > 1.28 and if Pvalue is less than 0.10.

a) Test statistic:

P-value:

The P-value is calculated using the excel formula for normal distribution which is =NORM.S.DIST(3.32, TRUE), thus the P-value is computed as 0.0004.

b) Conclusion:

Since P-value is less tahn 0.10 and the test statistic is greater than 1.28 hence we reject the null hypothesis and conclude that there is enough evdence to support the claim.