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NeX [460]
2 years ago
13

Assume that the following data were generated using a valid and appropriate methodology. XYZ Data Analytics, Inc. Received prope

rly completed surveys from 523 members of the target population for a new product. One hundred seventy nine of those respondents indicated they would buy the new product at the proposed price
Mathematics
1 answer:
Hitman42 [59]2 years ago
4 0

Using the z-distribution, as we are working with a proportion, the 95% confidence interval for the proportion of consumers who would buy the product at it's proposed price is (0.3016, 0.3830).

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

A confidence interval of proportions is given by:

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

In which:

  • \pi is the sample proportion.
  • z is the critical value.
  • n is the sample size.

In this problem, we have a 95% confidence level, hence\alpha = 0.95, 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.

179 out of 523 members indicated they would buy the new product at the proposed price, hence:

\pi = \frac{179}{523} = 0.3423

Then the bounds of the interval are found as follows:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3423 - 1.96\sqrt{\frac{0.3423(0.6577)}{523}} = 0.3016

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3423 + 1.96\sqrt{\frac{0.3423(0.6577)}{523}} = 0.3830

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

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