A researcher is interested in finding a 90% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 113 students who averaged 38.4 minutes concentrating on their professor during the hour lecture. The standard deviation was 11.7 minutes. Round answers to 3 decimal places where possible. a. To compute the confidence interval use a ? distribution. b. With 90% confidence the population mean minutes of concentration is between and minutes. c. If many groups of 113 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will SIAntain the true population mean minutes of concentration and about percent will not contain the true population mean minutes of concentration.

A researcher is interested in finding a 90% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 113 students who averaged 38.4 minutes concentrating on their professor during the hour lecture. The standard deviation was 11.7 minutes. Round answers to 3 decimal places where possible. a. To compute the confidence interval use a ? distribution. b. With 90% confidence the population mean minutes of concentration is between and minutes. c. If many groups of 113 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will SIAntain the true population mean minutes of concentration and about percent will not contain the true population mean minutes of concentration.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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### Understanding Confidence Intervals

A researcher is interested in finding a 90% confidence interval for the mean number of minutes students are concentrating on their professor during a one-hour statistics lecture. The study included 113 students who averaged 38.4 minutes concentrating on their professor during the one-hour lecture. The standard deviation was 11.7 minutes. Round answers to three decimal places where possible.

**Tasks:**

a. To compute the confidence interval, use a ___ distribution.

b. With 90% confidence, the population mean minutes of concentration is between ___ and ___ minutes.

c. If many groups of 113 randomly selected members are studied, then a different confidence interval would be produced from each group. About ___ percent of these confidence intervals will contain the true population mean minutes of concentration, and about ___ percent will not contain the true population mean minutes of concentration.

### Key Concepts:

- **Confidence Interval:** A range of values, derived from sample statistics, used to estimate the true population parameter.

- **90% Confidence Interval:** Indicates that if the same population is sampled multiple times, approximately 90% of the calculated intervals will contain the true population mean.

- **Standard Deviation:** A measure of the amount of variation or dispersion in a set of values.

This exercise provides a practical application of statistical methods to estimate the average student concentration time with a specified level of confidence.

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