Unit 5 Learning Content
A researcher wants to know the average age of everyone in Congress and he's short on time so he lists all the names of those serving in Congress and at random selects 10 of them for age data. Would this be considered a random sample?
Yes
The percentage of observations more than three standard deviations from the mean is
less than one percent
Suppose a researcher estimates the population value for average number of days a patient is sick with the flu. Which population parameter is being estimated:
mean
A Lake Tahoe Community College instructor is interested in the mean number of days Lake Tahoe Community College math students are absent from class during a quarter. What is the population she is interested in?
all Lake Tahoe Community College math students
The owner of a restaurant wants to know how customers like a new fish dish being served. He is busy tonight so he is only able to ask 5 of the customers who ordered the fish. What is the population of this study?
all customers who ate the new fish dish
A TV producer wants to know who subscribers of People magazine find the Sexiest Man Alive. The producer obtains a list of all subscribers and sends a questionnaire to 100 subscribers selected at random. Ninety questionnaires are returned. What is the population in this study?
all subscribers of people magazine
A trainer at YouFit wants to know how many times his clients train with him each month. Match the term on the left to the correct answer on the right.
data - values for x, such as 3,7, and so on population - all clients of this trainer parameter mean - the mean amount of time the client train each week with this trainer sample - a subset of this trainer's clients
The Miami Dolphins are one of the 35 teams in the NFL. This would be a:
data value
If our sample is not good, this can lead to an _____ in the estimation of our population.
error
A population parameter is:
estimated with range of values
A cardiologist is interested in the mean recovery period of her patients who have had heart attacks. What is the parameter of this study is:
mean recovery time of all her patients who have had heart attacks
A cardiologist is interested in the mean recovery period of her patients who have had heart attacks She collects data on only 50 of her patients who had heart attacks and finds that the mean recovery period was 5.7 years. What symbol would be used to designate the 50 patients?
n
A restaurant owner wants to know how customers who ordered the new fish dinner liked it. She is short on time so he questions the first 5 customers that try the fish. Would this be considered a simple random sample?
no
Every member of a group that fits our description is called the ______________.
population
Greek symbols refer to __________ values.
population
There are 30 teams in the NBA. The 30 teams would be considered a _________.
population
One way to reduce problems with our sample is to increase the ___________.
sample size
What is the most common way to collect a sample?
simple random sample
A Lake Tahoe Community College instructor is interested in the mean number of days Lake Tahoe Community College math students are absent from class during a quarter. The instructor's sample produces a mean number of days absent of 3.5 days. This value is an example of a:
statistic
When researchers analyze a sample, the claims they make are about
the population from which the sample was drawn
True or False: A confidence interval is found by adding and subtracting the margin of error to the point estimate.
true
True or False: a point estimate is one number
true
True/False: A confidence interval can be thought of as the estimate of a mean +/- an error term
true
True/False: Confidence intervals are based on a predetermined level of confidence (CL)
true
True/False: In most cases, Inferential statistics is the last step in the process of doing statistics
true
Use the following information to answer this exercise: A researcher is interested in knowing the average salary of a player on the Miami Marlins baseball team. In this example x= salary of a player on the team. In this case, x is an example of a:
variable
A survey finds that the average hospital stay for Hollywood Hospital is 4 days. Which of the following might be a good estimate for the hospital stay for all hospitals in the same town?
(3.8,4.2)
Assume the standard deviation for a sample is 3. If the sample size is 144, what is the Standard Error?
0.25
Suppose we have collected data from a sample. We know the sample mean, but we do not know the mean for the entire population. The sample mean is seven, and the margin of error is 2.5. Calculate the confidence interval:
4.5 9.5
The most commonly used level of confidence is
95%
A confidence interval is
A range of values centered on the mean
Which of the following is not a population?
All students in a randomly selected sample
There are 32 teams in the NFL (National Football League). Each team is based in a city in the United States. If we want to know the average salary for players on all 32 teams which of the following would best describe this value?
Population Parameter
We refer to any subset of a population as a ___________.
Sample
The owner of a restaurant wants to know how customers like a new fish dish being served. He is busy tonight so he is only able to ask 5 of the customers who ordered the fish. What is the sample of this study?
The 5 customers questioned by the manager customers who liked the dish
True/False: Inferential Statistics is the process of inferring facts about a population
True
Suppose scores on exams in statistics are normally distributed with an unknown population mean and a population standard deviation of three points. A random sample of 36 scores is taken and gives a sample mean (sample mean score) of 68. Using excel find the margin of error of a 90% confidence interval (give your answer to 4 decimal places):
0.8224 .8224
Suppose scores on exams in statistics are normally distributed with an unknown population mean and a population standard deviation of three points. A random sample of 36 scores is taken and gives a sample mean (sample mean score) of 68. Using excel find the margin of error of a 95% confidence interval (give your answer to 4 decimal places):
0.9800 .9800
Suppose scores on exams in statistics are normally distributed with an unknown population mean and a population standard deviation of three (3) points. A random sample of 36 scores is taken and gives a sample mean (sample mean score) of 68. Find the 95% confidence interval that estimates the population mean value.
67.02 68.98
Find the confidence interval that estimates the population mean if the sample mean is 68 and the margin of error is 0.8224. The 90% confidence interval is (give your answers to 4 decimal places):
67.1776 68.8224
What is true about Confidence Intervals?
A CI is used to estimate a population value based on a sample value
What is a confidence interval?
A range of values that are likely to contain a specified event
The formula for the standard error tells us:
As sample size increases the standard error comes closer to the population standard deviation
True/False: Inferential Statistics are useful because they do not require a good sample
False
True/False: When researchers analyze samples, it is because they want to state facts about those samples.
False
Which of the following is true of inferential statistics?
It allows statisticians to draw conclusions about the population.
Which of the following is true of a confidence level?
It is a pre-determined probability that specifies how confident a researcher wants to be that an event will be selected
Determine what the key terms refer to in the following study. A study was conducted at a local college to analyze the average cumulative GPAs of students who graduated last year. Match the phrase that best describes each of the items below.
Population - all students who graduated from the college last year Sample - a group of students who graduated from the college last year, randomly selected Data - 3.65, 2.80, 1.50, 3.90 Parameter - the average cumulative GPA of students who graduated from the college last year Variable - the cumulative GPA of students who graduated from the college last year Statistic - the average cumulative GPA of students in the study who graduated from the college last year
What are the key terms referred to in the following study: We want to know the average (mean) amount of money spent at Marlins baseball games by families with children. We randomly survey 100 families with children who attended at least one game at the new stadium. Three of the families spent $75, $85, and $95, respectively.
The POPULATION is all families with children attending a Marlins game. The SAMPLE is a random selection of 100 families with children attending a Marlins game. The PARAMETER is the average (mean) amount of money spent at Marlins games by families with children. The STATISTIC is the average (mean) amount of money spent at Marlins games by families in the sample.
The American Community Survey (ACS), part of the United States Census Bureau, conducts a yearly census similar to the one taken every ten years, but with a smaller percentage of participants. The most recent survey estimates with 90% confidence that the mean household income in the U.S. falls between $69,720 and $69,922. Find the point estimate for mean U.S. household income:
The margin of error is added to and subtracted from the sample mean to create the interval. The sample mean therefore is the average of the lower and higher values of the interval. (69922+69720)/2= 69821
Which of the following is an inferential statistic?
The mean income of the population of a state estimated using a representative sample
The owner of a restaurant wants to know how customers like the new fish dish being served. He is busy tonight so he is only able to ask 5 of the customers who ordered the fish; 60% liked the new fish dish. What is the parameter of this study?
The percentage of customers who ate the new fish dish and liked/disliked it
What is Standard Error?
The standard deviation of the population divided by the square root of the sample size
True/False: Inferential statistics can only tell us what is true about a population. It cannot tell us the accuracy of our claims.
false
What does the following symbol refer to: µ
population mean
What does the following symbol refer to: σ?
population standard deviation
One method to choose members of a simple random sample is:
randomly generated numbers
The most important feature of a good sample is that it is ________ of the population.
representative
In a study based on 100 dog owners at a recent dog fair, the most favorite breed of dog was the English Bulldog which was favored by 35%. The 100 dog owners in an example of:
sample
Only variables from the ______ can be measured.
sample
A cardiologist is interested in the mean recovery period of her patients who have had heart attacks She collects data on only 50 of her patients who had heart attacks and finds that the mean recovery period was 5.7 years. The 50 patients are called the _______________ of the study.
sample size
Determine what the key terms refer to in the following study. A study was conducted at a local college to analyze the average cumulative GPAs of students who graduated last year. Match the phrase that best describes each of the items below.
sample size
What does the following symbol refer to: s?
sample standard deviation
A cardiologist is interested in the mean recovery period of her patients who have had heart attacks. She collects data on only 50 of her patients who had heart attacks and finds that the mean recovery period was 5.7 years. The 5.7 years is called the _______________ of the study.
sample statistic
A study of dog owners found that, out of a sample of 100 owners, 30% of them had a pit bull. The 30% would be considered a:
sample statistic
The owner of a restaurant wants to know how customers like the new fish dish being served. He is busy tonight so he is only able to ask 5 of the customers who ordered the fish. Out of the 5 customers questioned by the manager, 60% of customers liked the new fish dish. The 60% is considered a:
statistic
A politician is interested in the proportion of voters in his district who think he is doing a good job. Match the term on the left to the correct answer on the right.
the parameter - the proportion of voters in this district who think this politician is doing a good job the statistic - the proportion of voters in the sample who think this politician is doing a good job the variable - x=the voters in the district who think this politician is doing a good job the data- yes, he is doing a good job. No, he is not doing a good job the sample - a random selection of voters in the politician's district the population - all voters in the politician's district
True/False: Increasing the size of a sample will reduce the size of the error when calculating the CI of a sample mean.
true
When building a CI for a sample mean, a researcher should use
use the standard error
A cardiologist is interested in the mean recovery period of her patients who have had heart attacks She collects data on only 50 of her patients who had heart attacks and finds that the mean recovery period was 5.7 years. 5.7 is an estimate of what value
μ
