Question

A researcher is interested in finding a 99% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 131 students who averaged 41.9 minutes concentrating on their professor during the hour lecture. The standard deviation was 13.8 minutes. Round answers to 3 decimal places where possible.

Answer 1

The 99% confidence interval for the mean number of minutes students concentrate during a statistics lecture, with a sample average of 41.9 minutes, standard deviation of 13.8 minutes, and sample size of 131, is approximately (38.784, 45.016) minutes.

Step-by-step explanation:

To calculate a 99% confidence interval for the mean number of minutes students are concentrating during a one-hour lecture, the following formula for the confidence interval of the mean when the population standard deviation is unknown is applied:

CI = \(\bar{x} \pm z \frac{s}{\sqrt{n}}\)

Where:

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Given data:

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From the standard normal distribution table, the z-score for a 99% confidence level is approximately 2.576.

Thus the confidence interval is calculated as follows:

CI = 41.9 \pm 2.576 \times \frac{13.8}{\sqrt{131}}

After calculating and rounding to three decimal places:

CI = (41.9 \pm 3.116)

Therefore, the 99% confidence interval is approximately (38.784, 45.016) minutes.