Sampling Distributions and the Central Limit Theorem

As the size of a sample increases, the standard deviation of the sampling distribution decreases.

• True

• False

A distribution showing the sample means of all sample of size n of a population is called

• Normal Distribution

• Binomial Distribution

• Sampling Distribution

• Uniform Distribution

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population

• The Sample

• The Sampling Distribution

The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week.  Let p-hat be the proportion of people in the sample who attended church.  A newspaper report claims that 40% of all U.S. adults went to church last week.  Suppose this claim is true. 
What is the mean of the sampling distribution of p-hat?

• 0.4

• 0.44

• 0.56

• 0.6

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25. 
What is the mean of the sampling distribution?

• 200

• 16

• 25

• 4

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25. 
What is the standard deviation of the sampling distribution?

• 200

• 16

• 25

• 4

Calculate μ_x-bar and σ_x-bar if μ = 794, σ = 48, and n = 64

• μ_x-bar = 794, σ_x-bar = 0.75

• μ_x-bar = 12.4, σ_x-bar = 0.75

• μ_x-bar =794, σ_x-bar = 6

• μ_x-bar = 99.25, σ_x-bar = 6

28% of all Suncoast students believe in Santa. You take a sample of 50 students and find that 15 of them believe in Santa. What does 15/50 represent?

• n

• P

• phat

• standard deviation

At a particular college, 78% of all students are receiving some kind of financial aid.The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving some sort of financial aid. Which of the following is true?

•  78% is a population and 72% is a sample.

• 72% is a population and 78% is a sample

• 78% is a parameter and 72% is a statistic

• 72% is a parameter and 78% is a statistic

The average cost for a gallon of gasoline is $2.51 (source AAA.org) with a standard deviation of $0.42. Find the mean and standard error of the sampling distribution if n = 49

• μ_x-bar = 2.51, σ_x-bar = 0.06

• μ_x-bar = 0.358, σ_x-bar = 0.06

• μ_x-bar = 2.51, σ_x-bar = 0.06

• μ_x-bar = 2.51, σ_x-bar = 0.857