Question

How much sugar do reduced sugar cookies typically have? You take a random sample of 51 reduced-sugar cookies and test them in a lab, finding a mean sugar content of 3.2 grams and a standard deviation of 1.1 grams of sugar. Create a 99% confidence interval for the mean grams of sugar.

Answer 1

Answer:  $(2.8,\ 3.6)$

Step-by-step explanation:

The confidence interval for population mean is given by :-

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

Given : Sample size : n= 51   ( >30 , that means its a large sample)

Sample mean : $\overlien{x}=3.2\text{ grams}$

Standard deviation : $\sigma=1.1\text{ grams}$

Significance level : $1-0.99=0.01$

Critical value : $z_{\alpha/2}=\pm2.576$

Now, the 99% confidence interval for the mean grams of sugar will be :-

$=3.2\pm(2.576)\times\dfrac{1.1}{\sqrt{51}}\\\\\approx3.2\pm0.40\\\\=(2.8,\ 3.6)$

Hence, the 99% confidence interval for the mean grams of sugar $\mu$ = $(2.8,\ 3.6)$