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.

Verified step by step guidance

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.
2. 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).
3. Substitute the values of \( x \) and \( n \) into the formula: \( \hat{p} = \frac{1740}{2096} \).
4. Simplify the fraction to calculate the proportion. This will give you the point estimate for the population proportion.
5. 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.

Key Concepts

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.

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.

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.