Question
14.You are testing chocolate chip cookies to estimate the mean number of chips per cookie. You sample 25 cookies and you find a sample mean of 10 chips per cookie. Assume the standard deviations is 2. Find a 95% confidence interval and explain what that means.
Answer
4.2
(200 Votes)
Kyla
Elite · Tutor for 8 years
Answer
The 95% confidence interval is calculated as follows:
Thus, the 95% confidence interval is:
This means we are 95% confident that the true mean number of chocolate chips per cookie lies between 9.216 and 10.784.
Explanation
To find a 95% confidence interval for the mean number of chocolate chips per cookie, we use the formula for the confidence interval of the mean: \( \bar{x} \pm z \left(\frac{\sigma}{\sqrt{n}}\right) \), where
is the sample mean,
is the z-score corresponding to the desired confidence level,
is the standard deviation, and
is the sample size. For a 95% confidence level, the z-score is approximately 1.96.