Sample Proportion and Population Proportion

Assume we have met all the pre-conditions to ensure our distribution of all possible sample proportions is normal. If I'm drawing a sample of size 100 (n=100) from a population that is 49% men (so p=.49), what is the probability that my sample proportion p-hat will be less than .40? Remember this proportion is normally distributed. 

P(p-hat<.40)=...

• .036

• .452

• .490

• .964

Given the same box of marbles with 28% red, if I randomly select 36 marbles what is the probability that I will have at least 9 red marbles in my sample? In this case p = 9/36 = .25 Hint: remember this is a "greater than or equal" problem

• Sample isn't large enough to use the normal distribution

• P(p-hat>.28) = .50

• P(p-hat>.28) = .66

• P(p-hat>.28) = .72

Newport News is 40% black. What is the probability that if we randomly selected 25 potential jury members for a trial, no more than 10 would be black?

• µ_p̂=.4, σ_p̂=.25, P(p̂<10/25)=P(p̂<.4)=0.72

• µ_p̂=.4, σ_p̂=.098, P(p̂<10/25)=P(p̂<.4)=0.50

• µ_p̂=.4, σ_p̂=.098, P(p̂<10/25)=P(p̂<.4)=0.37

Given an SRS of 30 math scores, what is an estimate of the true proportion of students in this population that score over 650 in math?

• One-Proprtion z-Test

• One-Proportion z-Interval

• One-Sample t-Interval

• One-Sample t-Interal on Matched Pairs

Which are necessary conditions to perform a significance test for a population proportion?

• Normal distribution of the population

• SRS from the population

• A sample size of at least 15

• A sample size that is less than 10% of the population size

Given an SRS of 20 math scores. Do we have reason to believe that the true proportion of students who score below 600 in math is not 50%?

• One-Proportion z-Test

• One-Sample t-Test

• One-Sample t-Test on Matched Pairs

• Two-Proportion z-Test

You wish to estimate, with 99% confidence, the population proportion of employees who prefer a four-day work week. Your estimate must be accurate to within 4% of the population proportion. What is the minimum required sample size if no preliminary estimate is available? Round up your answer to the nearest whole number.

• 1,036

• 1,037

• 422

• 423

You wish to estimate, with 90% confidence, the population proportion of adults who read fiction books. Your estimate must be accurate to within 2% of the population proportion. A prior study found that 47% of adults read fiction books. What is the minimum required sample size? Round up your answer to the nearest whole number.

You wish to estimate, with 99% confidence, the population proportion of employees who prefer a four-day work week. Your estimate must be accurate to within 4% of the population proportion. If no preliminary estimate is available, then what value should be used for the proportion of successes (Refer to the figure)?

• 0.5

• 0.01

• 0.04

• 0.99

You wish to estimate, with 99% confidence, the population proportion of employees who prefer a four-day work week. Your estimate must be accurate to within 4% of the population proportion. What is the margin of error (in decimal form)?