Use the normal distribution to find a confidence interval for a proportion p given the relevant sample results. Give the best point estimate for p, the margin of error, and the confidence interval. Assume the results come from a random sample. A 99% confidence interval for p given that p-hat = 0.34 and n= 500. Point estimate (2 decimal places) Margin of error (3 decimal places) The 99% confidence interval is to (3 decimal places)

(a) The point estimate for the population proportion p is 0.34.

(b) The margin of error for the 99% confidence interval of population proportion p is 0.055.

(c) The 99% confidence interval of population proportion p is (0.285, 0.395).

Step-by-step explanation:

A point estimate of a parameter (population) is a distinct value used for the estimation the parameter (population). For instance, the sample mean is a point estimate of the population mean μ.

Similarly, the the point estimate of the population proportion of a characteristic, p is the sample proportion .

The (1 - α)% confidence interval for the population proportion p is:

The margin of error for this interval is:

The information provided is:

(a)

Compute the point estimate for the population proportion p as follows:

Point estimate of p = = 0.34

Thus, the point estimate for the population proportion p is 0.34.

(b)

The critical value of z for 99% confidence level is:

*Use a z-table for the value.

Compute the margin of error for the 99% confidence interval of population proportion p as follows:

Thus, the margin of error for the 99% confidence interval of population proportion p is 0.055.

(c)

Compute the 99% confidence interval of population proportion p as follows:

Thus, the 99% confidence interval of population proportion p is (0.285, 0.395).

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