Question

Karen wants to advertise how many chocolate chips are in each big chip cookie at her bakery. she randomly selects a sample of 69 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 10.6 and a standard deviation of 1.7. what is the 95% confidence interval for the number of chocolate chips per cookie for big chip cookies? enter your answers accurate to 4 decimal places.

Answer 1

Answer: $(10.1989,\ 11.0011)$

Step-by-step explanation:

Given : Sample size : n=69

Sample mean : $\overline{x}=10.6$

Standard deviation : $s=1.7$

Significance level : $\alpha:1-0.95=0.05$

Then , Critical value : $z_{\alpha/2}=1.96$

The formula to confidence interval is given by : -

$\overline{x}\pm z_{\alpha/2}\dfrac{s}{\sqrt{n}}\\\\\Rightarrow\ 10.6\pm (1.96)\dfrac{1.7}{\sqrt{69}}\\\\\approx10.6\pm0.4011=(10.6-0.4011,10.6+0.4011)=(10.1989,\ 11.0011)$

Hence, the 95% confidence interval for the number of chocolate chips per cookie for big chip cookies= $(10.1989,\ 11.0011)$