Question

A researcher draws a population of 40 adults from a city and administers an IQ test (which is known to have a population mean of 100 and population standard deviation of 15). His sample mean is 108. What is the 95 percent confidence interval for this result?

Answer 1

Answer:
`(103.3515,\ 112.6485)`

Explanation:

According to the given information, we have

n= 40

`\sigma=15\\\\\overline{x}=108`

Critical z-value for 95% confidence =
`z_(\alpha/2)=1.96`

Confidence interval :

`\overline{x}\pm z_(\alpha/2)(\sigma)/(√(n))\\\\=108\pm (1.96)(15)/(√(40))\\\\\approx108\pm4.6485\\\\= (108-4.6485,\ 108+4.6485)\\\\=(103.3515,\ 112.6485)`

Hence, the 95 percent confidence interval for this result :
`(103.3515,\ 112.6485)`