Drug Concentration You are analyzing the times for the drug concentrations to peak in the patients in Exercise 14. The population standard deviation of the times for epinephrine concentrations to peak should be less than 10 minutes. Does the confidence interval you constructed for σ suggest that the variation in the times is at an acceptable level? Explain your reasoning.
Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 53m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample2h 19m
- 10. Hypothesis Testing for Two Samples3h 22m
- 11. Correlation1h 6m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
8. Sampling Distributions & Confidence Intervals: Proportion
Confidence Intervals for Population Proportion
Problem 6.T.1a
Textbook Question
In a survey of 2096 U.S. adults, 1740 think football teams of all levels should require players who suffer a head injury to take a set amount of time off from playing to recover. (Adapted from The Harris Poll)
a. Find the point estimate for the population proportion.

1
Identify the formula for the point estimate of a population proportion, which is given by \( \hat{p} = \frac{x}{n} \), where \( x \) is the number of successes (individuals with the desired characteristic) and \( n \) is the total sample size.
From the problem, note that \( x = 1740 \) (the number of adults who think players should take time off) and \( n = 2096 \) (the total number of surveyed adults).
Substitute the values of \( x \) and \( n \) into the formula: \( \hat{p} = \frac{1740}{2096} \).
Simplify the fraction to calculate the proportion. This will give you the point estimate for the population proportion.
Interpret the result: The point estimate represents the proportion of U.S. adults who believe football players should take time off after a head injury, based on the survey data.

This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Point Estimate
A point estimate is a single value that serves as a best guess or approximation of a population parameter. In this context, it refers to the proportion of U.S. adults who believe that football players should take time off after a head injury. The point estimate is calculated by dividing the number of individuals who support the idea by the total number of surveyed individuals.
Recommended video:
Introduction to Confidence Intervals
Population Proportion
The population proportion is the fraction of a population that possesses a certain characteristic. It is denoted by 'p' and is crucial for understanding the overall sentiment of a group. In this case, it represents the proportion of all U.S. adults who think players should take time off after a head injury, which can be estimated using survey data.
Recommended video:
Constructing Confidence Intervals for Proportions
Sample Size
Sample size refers to the number of observations or data points collected in a survey or study. A larger sample size generally leads to more reliable estimates of population parameters, as it reduces the margin of error. In this question, the sample size of 2096 adults is significant for calculating the point estimate and assessing the reliability of the findings.
Recommended video:
Sampling Distribution of Sample Proportion
Watch next
Master Constructing Confidence Intervals for Proportions with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice
Textbook Question
22
views