In the survey of 1500 students for the united states age 18 and under, 1043 were...

In the survey of 1500 students for the united states age 18 and under, 1043 were concerned about how they would pay for college.

a) Find the mean and standard deviation of those concerned about financing college.

b) Construct a 90% confidence interval for the population proportions. Interpret your results.

c) Find the minimum sample size needed to estimate the population proportion at the 99% confidence level in order to ensure that the estimate is accurate within 4% of the population proportion.

Solutions

Expert Solution

a) Given: X = 1043, n = 1500

Sample proportion

Let X denote the random variable with the event of success being that the students are concerned about how they would pay for college.

Since, X has a binary outcome, with independent trials,

Using property of Binomial Distribution:

Mean and Standard Deviation of those concerned about financing college are 1043 and 18 respectively.

b) 90% CI for population proportion is given by the formula:

......(For 90% CI, Z = 1.645)

= (0.676,0.715)

90% confidence interval for the population proportions is (0.676,0.715). If repeated samples are drawn, the true proportion would lie within this interval 90 out of 100 times.

c) The Margin of error given is 0.04

.......(For 99% CI, Z = 2.58)

The minimum sample size needed to estimate the population proportion at the 99% confidence level in order to ensure that the estimate is accurate within 4% of the population proportion is about 881.

orchestra answered 10 months ago

Next > < Previous

Related Solutions

survey of the MBA students at a university in the United States classified the country of...

survey of the MBA students at a university in the United States classified the country of origin of the students as seen in the table. Two-year MBA Evening MBA Total Asia 31 33 64 Europe 5 0 5 Latin America 20 1 21 Middle East 5 5 10 North America 103 65 168 Total 164 104 268 What percent of all MBA students were from North America? What percent of the Two-year MBA students were from North America? What percent...

A survey of 1057 parents who have a child under the age of 18 living at...

A survey of 1057 parents who have a child under the age of 18 living at home asked about their opinions regarding violent video games. A report describing the results of the survey stated that 89 % of parents say that violence in today's video games is a problem. (a) What number of survey respondents reported that they thought that violence in today’s video games is a problem? You will need to round your answer. X = (b) Find a...

A restaurant association says that households in the United States headed by people under the age...

A restaurant association says that households in the United States headed by people under the age of 25 spend less on food away from home than households headed by people ages 55-64. The mean amount spent per year by 32 households headed by people under the age of 25 is $2015 and the sample standard deviation is $113. The mean amount spent by 32 households headed by people ages 55-64 is $2715 and the sample standard deviation is $97. At...

The minimum legal drinking age in the United States is 21. Suppose we conduct a survey...

The minimum legal drinking age in the United States is 21. Suppose we conduct a survey of students at URI. We collect data on their age (in months), the number of drinks they consumed in the last week, number of minutes of exercise in the last week, their body mass index (BMI), and other characteristics such as education, race, gender, class year, etc. Using this observational data, what would be an appropriate identification strategy if we are interested in estimating...

QUESTION 2 Part 1 In a survey of 800 college students in the United States, 608...

QUESTION 2 Part 1 In a survey of 800 college students in the United States, 608 indicated that they believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action. Assuming that the sample is representative of college students in the United States, construct a 95% confidence interval for the proportion of college students who have this belief. (Use a table or technology. Round your answers to...

In a survey of 1000 randomly selected adults in the United States, participants were asked what...

In a survey of 1000 randomly selected adults in the United States, participants were asked what their most favorite and what their least favorite subject was when they were in school (Associated Press, August 17, 2005). In what might seem like a contradiction, math was chosen more often than any other subject in both categories! Math was chosen by 228 of the 1000 as the favorite subject, and it was also chosen by 366 of the 1000 as the least...

In a survey of 1000 randomly selected adults in the United States, participants were asked what...

In a survey of 1000 randomly selected adults in the United States, participants were asked what their most favorite and what their least favorite subject was when they were in school (Associated Press, August 17, 2005). In what might seem like a contradiction, math was chosen more often than any other subject in both categories! Math was chosen by 222 of the 1000 as the favorite subject, and it was also chosen by 362 of the 1000 as the least...

In United States, emergency contraception is available overt he counter to all women over age 18....

In United States, emergency contraception is available overt he counter to all women over age 18. What are the pros and cons of this decision?

In the early eighties, under the Reagan administration, macroeconomic policies in the United States were characterized...

In the early eighties, under the Reagan administration, macroeconomic policies in the United States were characterized by relatively expansionary fiscal policy (fueled by increased defense spending and tax cuts) and very tight monetary policy. Compared to an alternative policy mix which produced the same level of Y using more expansionary monetary policy and more contractionary fiscal policy. Contrast the two different policy mixes graphically and in words. Explain what effects you would expect such policy mixes to have on each...

at a party there are 25 students over age 21 and 15 students under age 21...

at a party there are 25 students over age 21 and 15 students under age 21 you choose a random five over those 21 and separately choose a random three of those under 21 to interview about attitudes towards alcohol. You've given every student at the party the same chance to be interviewed what is that chance. why is your sample not an SRS?

Subjects