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Anika [276]
2 years ago
14

Construct the indicated confidence interval for the population mean mu.

Mathematics
1 answer:
ExtremeBDS [4]2 years ago
3 0

Using the z-distribution, the confidence interval is given by: (11.95, 12.65).

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

\overline{x} \pm z\frac{\sigma}{\sqrt{n}}

In which:

  • \overline{x} is the sample mean.
  • z is the critical value.
  • n is the sample size.
  • \sigma is the standard deviation for the population.

In this problem, we have a 90% confidence level, hence\alpha = 0.9, z is the value of Z that has a p-value of \frac{1+0.9}{2} = 0.95, so the critical value is z = 1.645.

The other parameters are given as follows:

\overline{x} = 12.3, \sigma = 1.5, n = 50

Hence the bounds of the interval are:

\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 - 1.645\frac{1.5}{\sqrt{50}} = 11.95

\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 + 1.645\frac{1.5}{\sqrt{50}} = 12.65

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

#SPJ1

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