QuestionAugust 14, 2025

Dr. Kendi Sadek is an industrial psychologist. She is currently studying stress among executives of Internet companies. She has developed a questionnaire that she believes measures stress.score above 80 indicates stress at a dangerous level. A random sample of 15 executives revealed the following stress level scores. 94 78 83 90 78 99 97 90 97 90 93 94 100 75 84 Click here for the Excel Data File a. Find the point estimate of the population mean. Note: Round your answer to 2 decimal places. Estimated population mean square b. Construct a 95% confidence level for the population mean. Note: Round your answers to 2 decimal places. Confidence interval for the population mean is between square and square

Dr. Kendi Sadek is an industrial psychologist. She is currently studying stress among executives of Internet companies. She has developed a questionnaire that she believes measures stress.score above 80 indicates stress at a dangerous level. A random sample of 15 executives revealed the following stress level scores. 94 78 83 90 78 99 97 90 97 90 93 94 100 75 84 Click here for the Excel Data File a. Find the point estimate of the population mean. Note: Round your answer to 2 decimal places. Estimated population mean square b. Construct a 95% confidence level for the population mean. Note: Round your answers to 2 decimal places. Confidence interval for the population mean is between square and square
Dr. Kendi Sadek is an industrial psychologist. She is currently studying stress among executives of Internet companies. She
has developed a questionnaire that she believes measures stress.score above 80 indicates stress at a dangerous level.
A random sample of 15 executives revealed the following stress level scores.
94 78 83 90 78 99 97 90 97 90 93 94 100 75 84
Click here for the Excel Data File
a. Find the point estimate of the population mean.
Note: Round your answer to 2 decimal places.
Estimated population mean square 
b. Construct a 95%  confidence level for the population mean.
Note: Round your answers to 2 decimal places.
Confidence interval for the population mean is between square  and square

Solution
4.2(237 votes)

Answer

a. Estimated population mean = 90.13 ### b. Confidence interval for the population mean is between 85.84 and 94.42 Explanation 1. Calculate the Point Estimate of the Population Mean Add all scores and divide by the number of scores. The formula is \bar{x} = \frac{\sum x_i}{n}. 2. Calculate the Sample Standard Deviation Use the formula s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} to find the standard deviation. 3. Determine the Critical Value for a 95% Confidence Interval For a sample size of 15, use the t-distribution with 14 degrees of freedom. The critical value t_{0.025} is approximately 2.145. 4. Calculate the Margin of Error Use the formula E = t \cdot \frac{s}{\sqrt{n}}. 5. Construct the Confidence Interval The confidence interval is \bar{x} \pm E.

Explanation

1. Calculate the Point Estimate of the Population Mean<br /> Add all scores and divide by the number of scores. The formula is $\bar{x} = \frac{\sum x_i}{n}$.<br /><br />2. Calculate the Sample Standard Deviation<br /> Use the formula $s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$ to find the standard deviation.<br /><br />3. Determine the Critical Value for a 95% Confidence Interval<br /> For a sample size of 15, use the t-distribution with 14 degrees of freedom. The critical value $t_{0.025}$ is approximately 2.145.<br /><br />4. Calculate the Margin of Error<br /> Use the formula $E = t \cdot \frac{s}{\sqrt{n}}$.<br /><br />5. Construct the Confidence Interval<br /> The confidence interval is $\bar{x} \pm E$.
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