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Arada [10]
2 years ago
14

Salaries of 49 college graduates who took a statistics course in college have a​ mean, x overbar​, of $ 65 comma 300. Assuming a

standard​ deviation, sigma​, of ​$17 comma 805​, construct a 95​% confidence interval for estimating the population mean mu.
Mathematics
1 answer:
Molodets [167]2 years ago
7 0

Answer: 60,540< \mu

Step-by-step explanation:

The confidence interval for population mean is given by :-

\overline{x}-z^*\dfrac{\sigma}{\sqrt{n}}< \mu

, where \sigma = Population standard deviation.

n= sample size

\overline{x} = Sample mean

z* = Critical z-value .

Given :  \sigma=\$17,000

n= 49

\overline{x}= \$65,300

Two-tailed critical value for 95% confidence interval = z^*=1.960

Then, the 95% confidence interval would be :-

65,300-(1.96)\dfrac{17000}{\sqrt{49}}< \mu

=65,300-(1.96)\dfrac{17000}{7}< \mu

=65,300-4760< \mu

=60,540< \mu

Hence, the 95​% confidence interval for estimating the population mean (\mu) :

60,540< \mu

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