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Damm [24]
1 year ago
13

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

SAT
1 answer:
4vir4ik [10]1 year ago
4 0

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.

<h3>What is a confidence interval of proportions?</h3>

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

#SPJ1

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