Answered

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 :

JeanaShupp

Answer: [tex](103.3515,\ 112.6485)[/tex]

Step-by-step explanation:

According to the given information, we have

n= 40

[tex]\sigma=15\\\\\overline{x}=108[/tex]

Critical z-value for 95% confidence = [tex]z_{\alpha/2}=1.96[/tex]

Confidence interval :

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

Hence, the 95 percent confidence interval for this result : [tex](103.3515,\ 112.6485)[/tex]

Other Questions