Question

14 multiple choice 4 points construct the requested confidence interval. in a random sample of 60 computers, the mean repair cost was $150 with a standard deviation of $36. construct a 90% confidence interval for the population mean. ($537, $654) ($138, $162) ($141, $159) ($142, $158)

Explanation:

Step1: Determine the critical value

For a 90% confidence interval, the significance level \(\alpha = 1 - 0.90=0.10\), and \(\frac{\alpha}{2}=0.05\).
Since \(n = 60\) (\(n>30\)), we use the standard normal distribution \(z\). From the standard - normal table, \(z_{\frac{\alpha}{2}}=z_{0.05}\approx1.645\).

Step2: Calculate the margin of error

The formula for the margin of error \(E\) is \(E = z_{\frac{\alpha}{2}}\frac{s}{\sqrt{n}}\), where \(s = 36\), \(n = 60\).

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Step3: Calculate the confidence interval

The formula for the confidence interval for the population mean \(\mu\) is \(\bar{x}-E<\mu <\bar{x} + E\), where \(\bar{x}=150\).
\(\bar{x}-E=150 - 7.65=142.35\approx142\)
\(\bar{x}+E=150 + 7.65=157.65\approx158\)

Answer:

\((\$142,\$158)\)