Question

# 6.18 Is college worth it? Part II: Exercise 6.16 presents the results of a poll where...

6.18 Is college worth it? Part II: Exercise 6.16 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot afford it.

(a) Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context.
lower bound:_____ (please round to four decimal places)
upper bound:_____    (please round to four decimal places)

Interpret the confidence interval in context:

• 1. 90% of Americans choose not to go to college because they cannot afford it
• 2. We can be 90% confident that our confidence interval contains the sample proportion of Americans who choose not to go to    college because they cannot afford it
• 3. We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is    contained within our confidence interval

(b) Suppose we wanted the margin of error for the 90% confidence level to be about 1.5%. How large of a survey would you recommend?
A survey should include at least ______ people.

Solution :

Given that,

n = 331

Point estimate = sample proportion = = 48% = 0.48

1 - = 1 - 0.48 = 0.52

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 (((0.48 * 0.52) / 331 )

= 0.0452

A 90% confidence interval for population proportion p is ,

± E

= 0.48 ± 0.0452

= ( 0.4348, 0.5252 )

lower bound = 0.4348

upper bound = 0.5252

3. We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.

b) margin of error = E = 1.5% = 0.015

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.015)2 * 0.48 * 0.52

= 3001.88

sample size = n = 3002 people

#### Earn Coins

Coins can be redeemed for fabulous gifts.

Similar Homework Help Questions
• ### (3 points) Is college worth it? Among a simple random sample of 304 American adults who...

(3 points) Is college worth it? Among a simple random sample of 304 American adults who do not have a four-year college degree and are not currently enrolled in school, 137 said they decided not to go to college because they could not afford school. 1. Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context. Round to 4 decimal places. (...

• ### Among a simple random sample of 331 American adults who do not have a four-year college...

Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school. (a) A newspaper article states that only a minority of the Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey as evidence. Conduct a hypothesis test to...

• ### (1 point) Is college worth it? Part I Among a simple random sample of 331 American adults who do not have a four-year co...

(1 point) Is college worth it? Part I Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school. A newspaper article states that only a minority of the Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey...

• ### An article summarized results from a national survey of 2,402 Americans age 8 to 18. The...

An article summarized results from a national survey of 2,402 Americans age 8 to 18. The sample was selected to be representative of Americans in this age group. (Use a table or technology.) (a) of those surveyed, 1,125 reported owning a cell phone. Use this information to construct a 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own a cell phone. (Round your answers to three decimal places.) Interpret the interval. We are...

• ### 13. [-/7 Points] DETAILS PECKSTAT2 9.R.090. MY NOTES ASK YOUR TEACHER An article summarized results from...

13. [-/7 Points] DETAILS PECKSTAT2 9.R.090. MY NOTES ASK YOUR TEACHER An article summarized results from a national survey of 2,102 Americans age 8 to 18. The sample was selected to be representative of Americans in this age group. (Use a table or technology.) (a) of those surveyed, 1,226 reported owning a cell phone. Use this information to construct a 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own a cell phone. (Round...

• ### TV advertising agencies face increasing challenges in reaching audience members because viewing TV programs via digital streaming is gaining in popularity. A poll reported that 57% of 2343 American ad...

TV advertising agencies face increasing challenges in reaching audience members because viewing TV programs via digital streaming is gaining in popularity. A poll reported that 57% of 2343 American adults surveyed said they have watched digitally streamed TV programming on some type of device. (a) Calculate and interpret a confidence interval at the 99% confidence level for the proportion of all adult Americans who watched streamed programming up to that point in time. (Round your answers to three decimal places.)...

• ### What proportion of college students plan to major in Business? A 90% confidence interval is constructed...

What proportion of college students plan to major in Business? A 90% confidence interval is constructed based on data collected from 250 college students, and the interval is found to be from 0.18 to 0.27. Which of the following statements is a correct interpretation of this confidence interval? A We are confident that 90% of all students in the population plan to major in Business. B We are 90% confident the proportion of students in our sample who plan to...

• ### please answer #5 5. Ask Your In a survey on I experiences, 718 of 4003 adult...

please answer #5 5. Ask Your In a survey on I experiences, 718 of 4003 adult reported that they had seen or been with a ghost (a) What assumption must be made in order for it to be appropriate to use the formula of this section to construct a confidence interval to estimate the propartion of all adult Americans who have seen or been with a ghost? We need to assume that the 718 people are the only Americans who...

• ### The table provides summary statistics on highway fuel economy of cars manufactured in 2012 (from Exercise...

The table provides summary statistics on highway fuel economy of cars manufactured in 2012 (from Exercise 5.32). Use these statistics to calculate a 98% confidence interval for the difference between average highway mileage of manual and automatic cars, and interpret this interval in the context of the data. Mean SD Hwy MPG, Automatic 22.92 5.29 26 Hwy MPG, Manual 27.88 5.01 26 n 35 25 15 automatic manual Hwy MPG upper bound: lower bound: mpg (please round to two decimal...

• ### A survey of 1010 college seniors working towards an undergraduate degree was conducted. Each student was...

A survey of 1010 college seniors working towards an undergraduate degree was conducted. Each student was asked, "Are you planning or not planning to pursue a graduate degree?" Of the 1010 surveyed, 658 stated that they were planning to pursue a graduate degree. Construct and interpret a 98% confidence interval for the proportion of college seniors who are planning to pursue a graduate degree. (0.616,0.686): we are 98% confident that the proportion of college seniors who are planning to pursue...

Free Homework Help App

to Get Instant Free Answers
Need Online Homework Help?

Most questions answered within 3 hours.