Question

The following hypotheses are given.

H₀ : π ≤ 0.83
H₁ : π > 0.83

A sample of 140 observations revealed that p = 0.88. At the 0.05 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?

• Do not reject H₀.

• Reject H₀.

Answer 1

Sample size , n= 140

Sample proportion , p= 0.88

H₀ : π ≤ 0.83
H₁ : π > 0.83

Critical Value at 0.05 significane level = 1.96

Decision rule-   If the test statistic lie in between ( -1.96 , 1.96) we will fail to reject the null hypothesis, otherwise we will reject the null hypothesis.

Test statistic, z=    = = 1.574

Decision- Since the test statistic lie in the interval ( -1.96, 1.96), we will Fail to reject the null hypothesis.

Hence, Do not reject H₀.