Question

Catching goldfish for schoolCarly and Maysem plan to be preschool teachers after they graduate from college. To prepare for snack time, they want to know the mean number of goldfish crackers in a bag of original-flavored goldfish. To estimate this value, they randomly selected$12$ bags of original-flavored goldfish and counted the number of crackers in each bag. Here are their data:

Construct and interpret a $95\%$ confidence interval for the true mean number of crackers in a bag of original- flavored goldfish.

Short answer

The confidence interval is$(326.05,337.28)$.

Step-by-step solution

Given Information

It is given that data set is:

$317,330,325,323,335,337,324,342,330,349,335,333$

Concept Used

Formula Used is:

$\overline{x}-t_{\frac{a}{2},n-1}\times \frac{s}{\sqrt{n}}<\mu <\overline{x}+t_{\frac{a}{2},n-1}\times \frac{s}{\sqrt{n}}$

Calculation and Interpretation

• In MINTAB Sheet, enter data set.
• Press Stat>Basic Statistics>1-Sample t.
• Choose samples in Column. Select data.
• In confidence interval, enter $95\%$.
• Press OK.

Confidence Interval is $(326.05,337.28)$

There is $95\%$confidence that true mean lies between$326.05\text{and}337.28.$