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: $(103.3515,\ 112.6485)$

Step-by-step 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 :

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

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