Question

We love football! A Gallup poll conducted telephone interviews with a random sample of adults aged 18 and older. Data were obtained for 1000 people. Of these, 370 said that football is their favorite sport to watch on television.

a. Define the parameter p in this setting.

b. What point estimator will you use to estimate p? What is the value of the point estimate?

c. Do you believe that the value of the point estimate is equal to the value of p? Explain your answer.

Short answer

Part a) The parameter is the population proportion $p$is the proportion of adults aged $18$and older that think their favorite sport to watch on television is football.

Part b) The point estimate of population proportion is $37\%$

Part c) The point estimate of population proportion can be near to$p$

Step-by-step solution

Part a) Step 1: Given information

$$\begin{gathered} n=1000 \\ x=370 \end{gathered}$$

Part a) Step 1: Explanation

First, we must comprehend the concepts of population and parameter.

The population is the set of all possible individuals who share the trait of interest in a study.

A parameter is a numerical characteristic based on observations from a study's entire population of objects.

In this case, the parameter is the population proportion $p$, which is the proportion of adults aged $18$and older who believe football is their favorite sport to watch on television.

Part b) Step 1: given information

$$\begin{gathered} n=1000 \\ x=370 \end{gathered}$$

Sample proportion$\hat{p}=\frac{x}{n}$

Part b) Step 2: Calculation

The sample proportion is the population proportion's point estimate. This is found as,

$\hat{p}=\frac{370}{1000}=0.37=37\%$

Part c) Step 1: Given information

$\hat{p}=37\%$

Part c) Step 2: Calculation

The sample proportion is the population proportion's point estimate. The sample proportion of $37\%$is based on sample data, which is a subset of the population. Based on the entire population, different opinions may exist. As a result, we anticipate that the population proportion will be close to $37\%$