What is a sampling distribution?
Center and Variability
Proportions
Means
100
Parameters describe _____ and statistics describe ______.
populations and samples
100
True or false: The variability of a statistic increases as the sample size increases.
False
100
Why do we check the large counts condition?
To show that the sampling distribution of p-hat is approximately normal.
100
The ________ of the sampling distribution of x-bar measures how far the values of the sample mean typically vary from the population mean.
Standard deviation
200
The fact that different random samples of the same size from the same population produce different values of a statistic.
What is sampling variability?
200
The two characteristics of an unbiased estimator.
Low bias
Low variability
200
The makers of skittles claim that 20% of all Skittles candies are orange. You select a random sample of 30 skittles from a large bag. Let p-hat = the proportion of orange skittles in the sample.
Calculate the mean and standard deviation of the sampling distribution of p-hat.
200
A company uses a machine to fill plastic bottles with cola. The volume in a bottle follows an approximately normal distribution with a mean of mu = 298 ml and SD of 3 ml. Let x-bar be the sample mean volume in an SRS of 16 bottles.
Describe the shape, center, and variability of the sampling distribution of x-bar for samples of size 16.
Shape: approximately normal because the population distribution is approximately normal
Center:
Variability: 
300
Identify the following three statistics then give the symbols for the corresponding parameters.
x-bar is the sample mean
p-hat is the sample proportion
s sub x is the sample standard deviation
300
The blue line represents the parameter. Which of these graphs shows an unbiased estimator? Why?
i only
The mean of the sampling distribution is close to the parameter.
300
Quebec is the only province in Canada where the one official language is French. According to a recent census, 83.7% of Quebec residents identify French as their first language. You will select a SRS of 165 Quebec residents. Let p-hat be the proportion of residents in the sample who identify French as their first language.
Describe the shape center and variability of the sampling distribution.
Shape: approximately normal b/c of the LCC
Center: 
Variability: 
300
A company uses a machine to fill plastic bottles with cola. The volume in a bottle follows an approximately normal distribution with a mean of mu = 298 ml and SD of 3 ml. Let x-bar be the sample mean volume in an SRS of 16 bottles.
Find the 67th percentile of the sampling distribution of n=16.
298.33 ml
400
From a large group of people who each signed a card saying they intended to quit smoking, 1000 people were randomly selected. It turned out that 210 (21%) of the selected individuals had not smoked in the past 6 months.
Identify the population, parameter, sample and statistic.
Population: All people who signed a card saying they intended to quit smoking
Parameter: p = the true proportion of the population who quit smoking
Sample: The 1000 people chosen from those who signed the cards
Statistic: The proportion of the sample who quit smoking p-hat = 0.21
400
The average mile time for high school competitive male track runners in the US is 5.25 minutes with a standard deviation of 0.3 minutes. A student thinks that runners in Tallahassee are faster. To test this claim, he takes a random sample of 40 athletes and their best mile times from this track season.
Identify the population, parameter, sample and statistic.
Population: All male high school track runners in Tallahassee
Parameter: 
Sample: 40 runners
Statistic: The average mile time of the sample of runners
400
Quebec is the only province in Canada where the one official language is French. According to a recent census, 83.7% of Quebec residents identify French as their first language. You will select a SRS of 165 Quebec residents. Let p-hat be the proportion of residents in the sample who identify French as their first language.
What is the probability that less than 80% of the residents in the sample identify French as their first language?
z= -1.28
probability = 0.1003
400
A company uses a machine to fill plastic bottles with cola. The volume in a bottle follows an approximately normal distribution with a mean of mu = 298 ml and SD of 3 ml. Let x-bar be the sample mean volume in an SRS of 16 bottles.
In an SRS of size 16, find the probability that x-bar estimates mu to within plus or minus 1 ml.
For minus 1 ml, z = -1.33, area = 0.0918
For plus 1 ml, z = 1.33, area = 0.9082
Probability = 0.9082-0.0918 = 0.8164