QUESTIONS

Question 1

A research intern would like to estimate, with 90% confidence, the true proportion of employees who hold two jobs. No preliminary estimate is available. The researcher wants the estimate to be within 3% of the population mean.

The research intern has a table to use:

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

They complete the calculation for the minimum sample size as follows….

n= [1.645²(0.5)(0.5)] / 3²

≈0.075

Which the intern then rounds up to 1. Which value in the calculation is incorrect?

Question 2

A research intern would like to estimate, with 95% confidence, the true proportion of employees who are unsatisfied with their current job. No preliminary estimate is available. The researcher wants the estimate to be within 5% of the population mean.

The research intern has a table to use:

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

They complete the calculation for the minimum sample size as follows….

n= [1.96²(0.5)(0.5)] / 5²

≈0.038

Which the intern then rounds up to 1. Which value in the calculation is incorrect?

Question 3

Keisha wants to estimate the percentage of managers at her company that hold an MBA. She surveys 320 managers and finds that 70 hold an MBA.

Find the margin of error for the confidence interval for the population proportion with a 90% confidence level.

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Use the table of common z-scores above.

Round the final answer to three decimal places.

Question 4

An entertainment company surveyed 360 elementary school children and found that 153 of them were above grade-level readers. Find the standard error for the sample proportion of elementary school children who were above grade-level readers.

Enter your answer as a decimal rounded to three decimal places.

Question 5

In a recent survey of 500 social media users, 300 stated that they were concerned about privacy. Assuming the distribution is approximately normal, determine the point estimate and standard error for the proportion of social media users who are concerned about privacy.

Round your answers to three decimal places, as needed.

p′= 1

σp′= 2

Question 6

Richie wants to estimate the percentage of people who have a savings account. He surveys 300 individuals and finds that 234 have a savings account.

Find the margin of error for the confidence interval for the population proportion with a 90% confidence level.

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Use the table of common z-scores above.

Round the final answer to three decimal places.

Question 7

Emma wants to estimate the percentage of people who use public transportation in a city. She surveys 140 individuals and finds that 62 use public transportation.

Find the confidence interval for the population proportion with a 99% confidence level.

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Use the table of common z-scores above.

Round the final answer to three decimal places.

Question 8

Suppose 300 randomly selected people are surveyed to determine whether or not they rent their home. Of the 300 surveyed, 60 reported renting their home.

Find the confidence interval for the population proportion with a 99% confidence level.

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Use the table of common z-scores above.

Round the final answer to three decimal places.

Question 9

Suppose an advertising company wants to determine the current percentage of customers who read print magazines. How many customers should the company survey in order to be 98% confident that the estimated (sample) proportion is within 5 percentage points of the true population proportion of customers who read print magazines?

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Use the table of values above.

Question 10

Suppose a shoe store wants to determine the current percentage of customers who are males. How many customers should the company survey in order to be 90% confident that the estimated (sample) proportion is within 3 percentage points of the true population proportion of customers who are males?

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Use the table of values above.

Question 11

Suppose 420 randomly selected people are surveyed to determine whether or not they subscribe to cable TV. Of the 420 surveyed, 278 reported subscribing to cable TV.

Find the margin of error for the confidence interval for the population proportion with a 95% confidence level.

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Use the table of common z-scores above.

Round the final answer to three decimal places.

Question 12

Liz wants to estimate the percentage of people who rent their home. She surveys 320 individuals and finds that 176 rent their home.

Find the margin of error for the confidence interval for the population proportion with a 98% confidence level.

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Use the table of common z-scores above.

Round the final answer to three decimal places.

Question 13

In a recent survey of 79 heads of household, 46 said they did online banking on their cell phones. Find the standard error for the sample proportion of heads of household who do online banking on their cell phones.

Enter your answer as a decimal rounded to three decimal places.

Question 14

In a recent survey of 47 youth soccer players, 32 said that their favorite position to play is goalkeeper. Find the standard error for the sample proportion of soccer players whose favorite position is goalkeeper.

Enter your answer as a decimal rounded to three decimal places.

Question 15

Alice wants to estimate the percentage of people who plan on voting yes for the upcoming school levy. She surveys 380 individuals and finds that 260 plan on voting yes.

What is the correct interpretation of the confidence interval?

Question 16

Alice wants to estimate the percentage of people who plan on voting yes for the upcoming school levy. She surveys 380 individuals and finds that 260 plan on voting yes.

Identify the values needed to calculate a confidence interval at the 90% confidence level. Then find the confidence interval.

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Use the table of common z-scores above.

Round the final answer to three decimal places.

p′= 1

σp′ = 2

zα/2 = 3

(4, 5)

ANSWERS:

Question 1

The research intern has a table to use:

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

They complete the calculation for the minimum sample size as follows….

n= [1.645²(0.5)(0.5)] / 3²

≈0.075

Which the intern then rounds up to 1. Which value in the calculation is incorrect?

Answer

Question 2

The research intern has a table to use:

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

They complete the calculation for the minimum sample size as follows….

n= [1.96²(0.5)(0.5)] / 5²

≈0.038

Which the intern then rounds up to 1. Which value in the calculation is incorrect?

Answer

Question 3

Keisha wants to estimate the percentage of managers at her company that hold an MBA. She surveys 320 managers and finds that 70 hold an MBA.

Find the margin of error for the confidence interval for the population proportion with a 90% confidence level.

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Use the table of common z-scores above.

Round the final answer to three decimal places.

Answer

Margin of error = 0.038

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(Answer) MATH399N – Week 6 Assignment: Confidence Intervals for Population Proportion