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.

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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 1

The 95% confidence interval is calculated as follows: \[ \bar{x} \pm z \left(\frac{\sigma}{\sqrt{n}}\right) \] \[ 10 \pm 1.96 \left(\frac{2}{\sqrt{25}}\right) \] \[ 10 \pm 1.96 \left(\frac{2}{5}\right) \] \[ 10 \pm 1.96 \times 0.4 \] \[ 10 \pm 0.784 \] Thus, the 95% confidence interval is: \[ (10 - 0.784, 10 + 0.784) \] \[ (9.216, 10.784) \] This means we are 95% confident that the true mean number of chocolate chips per cookie lies between 9.216 and 10.784.

Answer 2

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 \( \bar{x} \) is the sample mean, \( z \) is the z-score corresponding to the desired confidence level, \( \sigma \) is the standard deviation, and \( n \) is the sample size. For a 95% confidence level, the z-score is approximately 1.96.

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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.

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