Question

Use the sample data and confidence level given below to complete parts a through d.

Answer 1

Using the information given and the z-distribution, it is found that:

a) The point estimate of the population proportion is 0.5544.

b) The margin of error is: 0.0320.

c) The interval is: (0.5224, 0.5864).

d) The interpretation of the interval is: we are 95% sure that the true population proportion is between 0.5224 and 0.5864.

What is a confidence interval of proportions?

A confidence interval of proportions has the bounds given by the rule presented as follows:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which the variables used to calculated these bounds are listed as follows:

• $\pi$ is the point estimate of the population proportion.

• z is the critical value.

• n is the sample size.

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$, so the critical value is z = 1.96.

From the sample, the sample size and the point estimate are given as follows:

$n = 929, \pi = \frac{515}{929} = 0.5544$

The margin of error is given by:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$M = 1.96\sqrt{\frac{0.5544(0.4456)}{929}}$

M = 0.0320.

The interval is the point estimate plus/minus the margin of error, hence:

• Lower bound: 0.5544 - 0.0320 = 0.5224.

• Upper bound: 0.5544 + 0.0320 = 0.5864.

More can be learned about the z-distribution at brainly.com/question/25890103

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