Question

A sample of 115 results in 46 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.)  

Point estimate

b. Construct 90% 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.)  

	Confidence Level Confidence Interval 90% to 99% to

c. Can we conclude at 90% confidence that the population proportion differs from 0.500?  

• Yes, since the confidence interval contains the value 0.500.

• Yes, since the confidence interval does not contain the value 0.500.

• No, since the confidence interval contains the value 0.500.

• No, since the confidence interval does not contain the value 0.500.

d. Can we conclude at 99% confidence that the population proportion differs from 0.500?

• No, since the confidence interval contains the value 0.500.

• No, since the confidence interval does not contain the value 0.500.

• Yes, since the confidence interval contains the value 0.500.

• Yes, since the confidence interval does not contain the value 0.500.

Answer 1

Given that, a sample of n = 115 results in x = 46 success.

a) The point estimate for the population proportion of success is,

46/115 = 0.400

=> point estimate = 0.400

b) A 90% confidence level has significance level of 0.10 and critical value is,

The 90% confidence interval for the population proportion is,

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

The 90% confidence interval for the population proportion is,

Therefore,

90% confidence interval : 0.325 to 0.475

99% confidence interval : 0.282 to 0.518

c) Since, 0.500 in not lies in 90% CI, we can conclude that the population proportion differs from 0.500

Answer : Yes, since the confidence interval does not contain the value 0.500

d) Since, 0.500 in lies in 99% CI, we can conclude that the population proportion is not differs from 0.500.

Answer : No, since the confidence interval contains the value 0.500.