MAT 131 Unit 4 HW Questions with Verified
Correct Answer
15.1 Genetic Engineering. Here's an idea for treating advanced melanoma, the most serious
kind of skin cancer: genetically engineer white blood cells to better recognize and destroy
cancer cells; then infuse these cells into patients. The subjects in a small initial study of this
approach were 11 patients whose melanoma had not responded to existing treatments. One
outcome of this experiment was measured by a test for the presence of cells that trigger an
immune response in the body and so may help fight cancer. The mean counts of active cells
per 100,000 cells for the 11 subjects were 3.8 before infusion and 160.2 after infusion. Is
each of the boldface numbers a parameter or a statistic?
Both are statistics; they came from the 11 subjects in the experiment.
15.3 Guns in School. Researchers surveyed 15,624 Amercian high school students (grades 9-
12) and found that 27.2% of those surveyed were in grade 9. The percent of all American
high school students who are in grade 9 is 27.5%. The percent of those surveyed who were
in grade 9 and had carried a gun to school was 4.5%. Is each of the boldface numbers a
parameter or a statistic?
27.2% and 4.5% are statistics (they are based on the survey of 15,624 American high school
students); 27.5% is a parameter (it is based on all American high school students).
15.5 Insurance. The idea of insurance is that we all face risks that are unlikely but carry
high cost. Think of a fire or flood destroying your apartment. Insurance spreads the risk:
we all pay a small amount, and the insurance policy pays a large amount to those few of us
whose apartments are damaged. An insurance company looks at the records for millions of
, apartment owners and sees that the mean loss
from apartment damage in a year is μ = 130 per person. (Most of us have no loss, but a few
lose most of their possessions. The $130 is the average loss.) The company plans to sell
renter's insurance for $130 plus enough to cover its costs and profit. Explain clearly why it
would be unwise to sell only 10 policies. Then explain why selling thousands of such policies
is a safe business.
Although the probability of having to pay for a total loss for one or more of the 10 policies is
very small, if this were to happen, it would be financially disastrous. For thousands of policies,
the law of large numbers says that the average claim on many policies will be close to the mean,
so the insurance company can be assured that the premiums they collect will (almost certainly)
cover the claims.
15.7 Generating a Sampling Distribution. Let's illustrate the idea of a
sampling distribution in the case of a very small sample from a very small population. The
population is the scores of 10 students on an exam:
The parameter of interest is the mean score μ in this population. The sample is an SRS of
size n = 4 drawn from the population. The Simple Random Sample applet can be used to
select simple random samples of four numbers between 1 and 10, corresponding to the
students.
(a) Make a histogram of these 10 scores.
(b) Find the mean of the 10 scores in the population. This is the population mean μ.
(c) Use the Simple Random Sample applet to draw an SRS of size 4 from this population.
What are the four scores in your sample? What is their mean x ̄? This statistic is an
Correct Answer
15.1 Genetic Engineering. Here's an idea for treating advanced melanoma, the most serious
kind of skin cancer: genetically engineer white blood cells to better recognize and destroy
cancer cells; then infuse these cells into patients. The subjects in a small initial study of this
approach were 11 patients whose melanoma had not responded to existing treatments. One
outcome of this experiment was measured by a test for the presence of cells that trigger an
immune response in the body and so may help fight cancer. The mean counts of active cells
per 100,000 cells for the 11 subjects were 3.8 before infusion and 160.2 after infusion. Is
each of the boldface numbers a parameter or a statistic?
Both are statistics; they came from the 11 subjects in the experiment.
15.3 Guns in School. Researchers surveyed 15,624 Amercian high school students (grades 9-
12) and found that 27.2% of those surveyed were in grade 9. The percent of all American
high school students who are in grade 9 is 27.5%. The percent of those surveyed who were
in grade 9 and had carried a gun to school was 4.5%. Is each of the boldface numbers a
parameter or a statistic?
27.2% and 4.5% are statistics (they are based on the survey of 15,624 American high school
students); 27.5% is a parameter (it is based on all American high school students).
15.5 Insurance. The idea of insurance is that we all face risks that are unlikely but carry
high cost. Think of a fire or flood destroying your apartment. Insurance spreads the risk:
we all pay a small amount, and the insurance policy pays a large amount to those few of us
whose apartments are damaged. An insurance company looks at the records for millions of
, apartment owners and sees that the mean loss
from apartment damage in a year is μ = 130 per person. (Most of us have no loss, but a few
lose most of their possessions. The $130 is the average loss.) The company plans to sell
renter's insurance for $130 plus enough to cover its costs and profit. Explain clearly why it
would be unwise to sell only 10 policies. Then explain why selling thousands of such policies
is a safe business.
Although the probability of having to pay for a total loss for one or more of the 10 policies is
very small, if this were to happen, it would be financially disastrous. For thousands of policies,
the law of large numbers says that the average claim on many policies will be close to the mean,
so the insurance company can be assured that the premiums they collect will (almost certainly)
cover the claims.
15.7 Generating a Sampling Distribution. Let's illustrate the idea of a
sampling distribution in the case of a very small sample from a very small population. The
population is the scores of 10 students on an exam:
The parameter of interest is the mean score μ in this population. The sample is an SRS of
size n = 4 drawn from the population. The Simple Random Sample applet can be used to
select simple random samples of four numbers between 1 and 10, corresponding to the
students.
(a) Make a histogram of these 10 scores.
(b) Find the mean of the 10 scores in the population. This is the population mean μ.
(c) Use the Simple Random Sample applet to draw an SRS of size 4 from this population.
What are the four scores in your sample? What is their mean x ̄? This statistic is an
