Question

A sample of 160 results in 40 successes. [You may find it useful to reference the z table.]

a. Calculate the point estimate for the population proportion of successes. (Do not round intermediate calculations. Round your answer to 3 decimal places.)

b. Construct 95% and 99% confidence intervals for the population proportion. (Round intermediate calculations to at least 4 decimal places. Round "z" value and final answers to 3 decimal places.)

c. Can we conclude at 95% confidence that the population proportion differs from 0.310? (multiple choice)

No, since the confidence interval does not contain the value 0.310.

No, since the confidence interval contains the value 0.310.

Yes, since the confidence interval does not contain the value 0.310.

Yes, since the confidence interval contains the value 0.310.

d. Can we conclude at 99% confidence that the population proportion differs from 0.310? (Multiple choice)

No, since the confidence interval contains the value 0.310.

No, since the confidence interval does not contain the value 0.310.

Yes, since the confidence interval contains the value 0.310.

Yes, since the confidence interval does not contain the value 0.310.

Answer #1

Given that, a sample of 160 results in 40 successes.

a) The point estimate for the population proportion of successes
= 40/160 = **0.250**

b) A 95% confidence level has significance level = 0.05 and critical value is,

95% confidence interval for p is,

The 95% CI is, (0.1829, 0.3171)

A 99% confidence level has significance level = 0.01 and critical value is,

99% confidence interval for p is,

The 99% CI is, (0.1619, 0.3381)

c) No, since the confidence interval contains the value 0.310

d) No, since the confidence interval contains the value 0.310

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