Suppose the length, in words, of the essays written for a contest are normally distributed and have a known population standard deviation of 325 words and an unknown population mean. A random sample of 25 essays is taken and gives a sample mean of 1640 words. Identify the parameters needed to calculate a confidence interval at the 98% confidence level. Then find the confidence interval.

Respuesta :

Answer:

(1589.55,1791.45)

Step-by-step explanation:

Given that, population standard deviation = 325 words

sample size ( n ) = 25 and sample mean = 1640 words

A 98% confidence level has significance level of 0.02 and critical value is, Z* = 2.33

The 98% confidence interval for population mean is,

[tex]1640- 2.33\times\frac{325}{\sqrt{25} } <\mu<1640+2.33\times\frac{325}{\sqrt{25} }[/tex]

1640-151.45<μ<1640+151.45

1589.55<μ<1791.45

therefore the confidence interval is (1589.55,1791.45)