Question

America’s favorite cookie Ann and Tori wanted to estimate the average weight of an Oreo cookie to determine if it was less than advertised (34 grams for 3 cookies). They selected a random sample of $36$cookies and found the weight of each cookie (in grams). The mean weight was $x̄=11.3921$grams with a standard deviation of $s_X=0.0817$grams. Construct and interpret a $90\%$confidence interval for the true mean weight of an Oreo cookie.

Short answer

The confidence interval is$(11.37,11.42)$.

Step-by-step solution

Given Information

It is given that $\left(\overline{x}\right)=11.3921$

$\left(s_x\right)=0.0817$

$n=36$

Concept Used

$t$confidence interval for population mean is calculated as:

$CI=\overline{x}\pm t_{\alpha /2,df}\times \frac{s}{\sqrt{n}}$

Calculation

As standard deviation is not known, $t$confidence interval is used.

Excel gives output as:

Confidence Interval is$(11.37,11.42)$