Question

5.4 Unexpected expense. In a random sample 765 adults in the United States, 322 say they could not cover a $400 unexpected expense without borrowing money or going into debt.(a) What population is under consideration in the data set?(b) What parameter is being estimated?(c) What is the point estimate for the parameter?

Answer 1

Answer : (a) All adults in the United States.

(b)The proportion (p) of people who could not cover a $400 unexpected expense without borrowing money or going into debt.

(c) 0.421

Explanation:

In a random sample 765 adults in the United States, 322 say they could not cover a $400 unexpected expense without borrowing money or going into debt.

• A population is the set of all possible individuals as researchers point of interest. A sample is a finite subset of the population.

Since , sample is of 765 adults in the United States.

So , the population of interest is "all adults in United states".

• The parameter is a number that summarize the population as per objective of the study.

Since , out of 765 adults in the United States, 322 say they could not cover a $400 unexpected expense without borrowing money or going into debt.

⇒ The parameter is the population proportion (p) of people who could not cover a $400 unexpected expense without borrowing money or going into debt.

Sample proportion of say they could not cover a $400 unexpected expense without borrowing money or going into debt. :
`\hat{p}=(322)/(765)\approx0.421` .

Since the sample proportion is the best point-estimate of the population proportion.

Therefore , the point estimate for the parameter is 0.421.

Answer 2

The population is under consideration in the data set is 765 adults in the United States.

The parameter must be the proportion of people who could not cover a $400 unexpected expense without borrowing money or going into debt.

The point estimated for the parameter is 0.421

Explanation:

Consider the provided information.

In a random sample 765 adults in the United States, 322 say they could not cover a $400 unexpected expense without borrowing money or going into debt.

Part (A) What population is under consideration in the data set?

A population is refer to the total set of observation.

Since, the total adults in the data set is 765.

Thus, the population is under consideration in the data set is 765 adults in the United States.

Part (B) What parameter is being estimated?

The parameter is any number that characterizes the population in question.

322 say they could not cover a $400 unexpected expense without borrowing money or going into debt.

That means the parameter must be the proportion of people who could not cover a $400 unexpected expense without borrowing money or going into debt.

Hence, the parameter must be the proportion of people who could not cover a $400 unexpected expense without borrowing money or going into debt.

Part (C) What is the point estimate for the parameter?

We can calculate the point estimate by dividing the number of people could not cover a $400 unexpected expense with total number of adults.

`(322)/(765) \approx 0.421`

Hence, the point estimated for the parameter is 0.421