Question

Hypotheses for a statistical test are given along with a confidence interval for a sample. Use the confidence interval to state a formal conclusion of the test for that sample and give the significance level used to make the conclusion.

                                 Ho: p = 0.5 vs Ha: p ≠ 0.5

1. 1. 95% confidence interval for p: 0.36 to 0.55.
2. 2. 90% confidence interval for p: 0.32 to 0.48.
3. 3. 99% confidence interval for p: 0.18 to 0.65.

Answer 1

Solution:

Hypothesis about population proportion p are

Ho: p = 0.5 vs Ha: p ≠ 0.5

Two tailed test

a)

95% confidence interval for p: 0.36 to 0.55.

The hypothetical value 0.5 is inside the interval.

So ,

Do not reject Ho: p = 0.5

Conclusion: At = 0.025 , there is no evidence to conclude that the population proportion is different from 0.5

b)

90% confidence interval for p: 0.32 to 0.48.

The hypothetical value 0.5 is not inside the interval.

So ,

Reject Ho: p = 0.5

Conclusion: At = 0.05 , there is sufficient evidence to conclude that the population proportion is different from 0.5

c)

99% confidence interval for p: 0.18 to 0.65.

The hypothetical value 0.5 is inside the interval.

So ,

Do not reject Ho: p = 0.5

Conclusion: At = 0.005 , there is no evidence to conclude that the population proportion is different from 0.5