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Rudik [331]
3 years ago
11

Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 20

part-time workers had mean annual earnings of $3120 with a standard deviation of $677. Round to the nearest dollar.
Business
1 answer:
miv72 [106K]3 years ago
4 0

Answer: (2823, 3417)

Explanation:

The confidence interval for the population mean is given by :-

\mu\ \pm E, where E is the margin of error.

Formula for Margin of error :-

z_{\alpha/2}\times\dfrac{\sigma}{\sqrt{n}}

Given : Significance level : \alpha=1-0.95=0.05

Sample size = 20

\mu=3120

\sigma=677

Critical value : z_{\alpha/2}=z_{0.025}=\pm1.96

Margin of error : E=1.96\times\dfrac{677}{\sqrt{20}}\approx 297

Now, the 95% confidence interval for the population mean will be :-

3120\ \pm\ 297 =(3120-297\ ,\ 3120+297)=(2823,\ 3417)

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