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IrinaK [193]
3 years ago
9

A university surveyed recent graduates of the English department about their starting salaries. Four hundred graduates returned

the survey. The average salary was $25,000. Assume for purposes of this problem that the population standard deviation is known, and it is $2,500. What is the 95% confidence interval for the mean salary of all graduates from the English department?
Mathematics
1 answer:
Dafna1 [17]3 years ago
8 0

Answer:   (24755, 25245)

Step-by-step explanation:

Given : Sample size : n= 400

Sample mean : \overline{x}= \$25,000

Standard deviation : \sigma=\$2,500

Significance level : \alpha: 1-0.95=0.05

Critical value : z_{\alpha/2}=1.96

The confidence interval for population mean is given by :-

\overline{x}\pm\ z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=25000\pm(1.96)\dfrac{2500}{\sqrt{400}}\\\\=25000\pm245\\\\=(25000-245,\ 25000+245)=(24755,\ 25245)

Hence, the 95% confidence interval for the mean salary of all graduates from the English department is (24755, 25245)

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