A random sample of 10 motorists buying petrol are found to spend an average of £58.30 with estimated standard error £5.25. Calculate a 95% confidence interval for the expected spending of motorists at this petrol station.
I got 10 of these questions so if someone can help me do this one i think i can do the rest. Thanks in advance.
Your interval is defined by $$\left(\overline x-z^*\frac{\sigma}{\sqrt{N}},\space\overline x+z^*\frac{\sigma}{\sqrt{N}}\right)$$ You already know $\overline x = 58.3, \space N=10, \space\sigma = 5.25$. Your $z^*$ value is determined by how wide you want your confidence interval. Since you want a $95\%$ interval and know that $95\%$ of a normally distributed population is contained within $1.96$ standard deviations from the mean, you want $z^* = 1.96$. The rest is just a matter of plugging in numbers. Your sample size is extremely small, so you may also want to make a note of that in your answer.
