Question

The dataset Restaurant Tips contains data recorded from 157 restaurant bills at a bistro in New York over a two week period and is considered to be representative of all bills at this particular restaurant. The mean tip was $3.849 and the standard deviation was 2.421. Using the methods of Section 6.2-CI (statistic ± t*(SE)), find and interpret a 90% confidence interval for the average tip given at this restaurant. Show all calculations.

Answer 1

Answer: ($3.532, $4.166)

Step-by-step explanation:

Given : Significance level : $\alpha: 1-0.90=0.10$

Critical value : $z_{\alpha/2}=1.645$

Sample size : n= 157

Sample mean : $\overline{x}=\ \ 3.849$

Standard deviation : $\sigma= \ \ 2.421$

The confidence interval for population mean is given by :_

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

$\text{i.e. }\ \ 3.849\pm (1.64)\dfrac{2.421}{\sqrt{157}}\\\\\approx\ \ 3.849\pm0.317\\\\=(\ \ 3.849-0.317,\ \ 3.849+0.317)=(\ \ 3.532,\ \ 4.166)$

Hence, the 0% confidence interval for the average tip given at this restaurant = ($3.532, $4.166)