Sample Proportions

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

Assume we are sampling to find the percent of people of Asian descent from a population that is actually 20% Asian (p=.2). Which of the following sample sizes would meet the minimum requirement for assuming the distribution of sampling proportions is normal? (Hint-remember your pre-conditions). Select ALL that would be considered big enough.

• 10

• 20

• 50

• 75

Given a population with proportion p=.35. Which of the following is true of a sample of size 50? Assume the sample is taken randomly and all individuals are independent of each other, and we have not violated the 10% rule.

• Pre-conditions for normality have not been met (the sample is too small).

• Sample is big enough, p= .50 and sampling distribution = .35

• Sample is big enough, p= .35 and sampliing distribution = .067

• Sample is big enough, p= .35 and the sampling distribution = .107

Given a box of 1000 marbles that is 28% red, if I randomly select 36 marbles, have I drawn a large enough sample to use the normal distribution?

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

Sigma of P-Hat

• Population Standard Deviation

• Standard Deviation of the Sampling Distribution of Sample Means

• Sample Percents of the Standard Deviation

• Standard Deviation of the Sampling Distribution of Sample Proportions

What does this formula do?

• Calculates Standard Deviation for Sampling Dist. of Sample Means

• Checks if the samples are independent

• Checks Normality

• Calculates Standard Deviation for Sampling Dist. of Sample Proportions

Select the correct description

• Mean of the Sampling Distribution of p-hat

• Population Mean

• Percents of Means

• Proportions

Which best describes the sampling distribution shown below.

• Unbiased Estimator

• Biased Estimator