Question 1

In a few sentences, describe the difference between statistical and practical
significance.

Accepted Answer

The answer of In a few sentences, describe the difference...

Question 2

As $n$ increases, the mean of the sampling distribution of $\bar { x }$ gets closer to $\mu$.

Accepted Answer

A) True 
 B)False

Question 3

T The foraging capability of Downy Woodpeckers can be compromised if part of their habitat disappears due to significant human encroachment. These creatures eat insects in trees, and if they cannot find enough food due to a decreasing forest area their body mass may decrease. A previous study of Downy Woodpeckers indicates that for male Downy Woodpeckers the population standard deviation of body mass is approximately $1.5 \mathrm {~g}$. Suppose that an estimate $\mu$, the current average mass of male Downy Woodpeckers in a local forest preserve, is desired. If the previous study value is taken as a reasonable first estimate of the population standard deviation, what is the minimum sample size that is necessary to estimate $\mu$ to within $0.2$ grams with $95 \%$ confidence?

Accepted Answer

The answer of T The foraging capability of Downy Woodpeckers...

Question 4

C Consider sampling from a normal population with a population mean $\mu$ and standard deviation $\sigma$. As the sample size, $n$, increases, some characteristics of the sampling distribution of the sample mean, $\bar { x }$, may change. Which of the following characteristics will change as $n$ increases, and what is the nature of the change?
a) The mean of the sampling distribution of $\bar { x }$

b) The standard deviation of the sampling distribution of $\bar { x }$

c) The shape of the sampling distribution of $\bar { x }$

Accepted Answer

The answer of C Consider sampling from a normal population...

Question 5

When performing hypothesis tests, there are assumptions that must be met in order for the test
to be appropriate. Describe the assumptions associated with a hypothesis test about a
population mean when the sample size is small. For any assumptions that can be checked
using sample data, describe how the check would be performed.

Accepted Answer

The answer of When performing hypothesis tests, there are assumptions...

Question 6

The $t$ confidence interval formula for estimating $\mu$ is appropriate when the population being sampled is approximately normally distributed.

Accepted Answer

A) True 
 B)False

Question 7

A company provides portable walkie-talkies to construction crews. Their batteries last, on
average, 55 hours of continuous use. The purchasing manager receives a brochure
advertising a new brand of batteries with a lower price, but suspects that the lifetime of the
batteries may be shorter than the brand currently in use. To test this, 8 randomly selected
new brand batteries are installed in the same model radio. Here are the results for the
lifetime of the batteries (in hours): $$\begin{array} { l l l l l l l l } 
45 & 52 & 56 & 55 & 51 & 57 & 48 & 52
\end{array}$$ Is there sufficient evidence to conclude that the purchasing manager is correct in his
conjecture that the new brand has a shorter average lifetime?

Accepted Answer

The answer of A company provides portable walkie-talkies to construction...

Question 8

A new species of sea crab has been discovered, and a study was conducted to determine whether or not the animal can regulate its temperature. If the animal can maintain a body temperature different from the surroundings, this would be considered evidence of regulating capability. Ten of these sea crabs were exposed to ambient temperatures of 24 degrees Celsius and their body temperatures were measured. The sample mean was $24.694$ degrees, and the standard deviation $0.277$ degrees.

For purposes of this example, assume that it is reasonable to regard these 10 crabs as a random sample from the population of all crabs of this species. A plot of the data indicated that the assumption of approximately normal body temperatures was credible.
a) Construct and interpret a $99 \%$ confidence interval for the mean body temperature, $\mu$.

b) Based on your answer to part (a), does it appear that the crabs are able to regulate their body temperature? Provide statistical justification for your response.

Accepted Answer

The answer of A new species of sea crab has...

Question 9

A A random sample of size $n = 25$ is selected from a population with mean $\mu = 50$ and standard deviation $\sigma = 10$. Determine the mean and standard deviation of the sampling distribution of $\bar { x }$.

Accepted Answer

The answer of A A random sample of size \(n...

Question 10

In a few sentences, describe the difference between statistical and practical
significance.

Accepted Answer

The answer of In a few sentences, describe the difference...

Question 11

A statistic is a characteristic of a population.

Accepted Answer

A) True 
 B)False

Question 12

A boat manufacturer claims that a particular boat model and motor combination will
burn less than 4.0 gallons of fuel per hour. Fuel consumption for a random sample of
10 similar boats was measured, resulting in the data below: $$4.06,4.29,4.26,4.64,4.23,3.93,3.64,4.13,3.93,3.86$$ A consumer group is interested in determining if there is convincing evidence that the
manufacturer's claim is correct.
a) What null and alternative hypotheses should the investigators use? In a few
sentences, justify your choice of the alternative hypothesis.
b) Using a graphic technique of your choice, show that the t-procedures are
appropriate to use with these data. c) Using your hypotheses from part (a), carry out a hypothesis test using $\alpha = 0.05$ and interpret the results. d) In the context of this study, describe a Type I and a Type II error.

Accepted Answer

The answer of A boat manufacturer claims that a particular...

Question 13

We say that the result of a hypothesis test is "statistically significant"
when the P-value is less than or equal toα.

Accepted Answer

A) True 
 B)False

Question 14

C Consider sampling from a normal population with a population mean $\mu$ and standard deviation $\sigma$. As the sample size, $n$, increases, some characteristics of the sampling distribution of the sample mean, $\bar { x }$, may change. Which of the following characteristics will change as $n$ increases, and what is the nature of the change? a) The mean of the sampling distribution of $\bar { x }$

b) The standard deviation of the sampling distribution of $\bar { x }$

c) The shape of the sampling distribution of $\bar { x }$

Accepted Answer

The answer of C Consider sampling from a normal population...

Question 15

A simple random sample of 10 houses in a particular town was selected and the level of radon gas measured for each house in the sample. The sample mean was $7.7$ parts per million, and the standard deviation $2.98$ parts per million. Experience has shown that radon gas level is approximately normally distributed in similar populations.
a) Construct and interpret a $99 \%$ confidence interval for $\mu$.
b) The city standards for radon call for a radon level of no more than $6 \mathrm { ppm }$. Based on your answer to part (a), does it appear that the mean radon level for city houses is greater than 6 ppm? Provide statistical justification for your response.

Accepted Answer

The answer of A simple random sample of 10 houses...

Question 16

If the null hypothesis is not rejected, there is strong statistical evidence
that the null hypothesis is true.

Accepted Answer

A) True 
 B)False

Question 17

At the Billy Goat Gruff Inn, machines are set to dispense 600 ml of soda into every
customer's glass. Over time, however, the machine can get "out of control" and dispense too
much soda or too little. The machine needs adjustment if the mean amount dispensed is
different than 600 ml. At a randomly selected time each clock hour, the owner dispenses and
checks a glass of soda and determines the actual volume of soda dispensed. One day the
volumes (in ml) of the dispensed soda were: $$600.15,599.92,599.85,599.92,599.81,600.14,600.04,599.98$$ Is there sufficient evidence to conclude that the dispensing machine needs adjustment?

Accepted Answer

The answer of At the Billy Goat Gruff Inn, machines...

Question 18

The department of natural resources classifies a fish to be unsafe to eat if its
polychlorinated biphenol (PCB) concentration exceeds 5 parts per billion (ppb). A
random sample of 10 fish taken from a local lake resulted in the concentrations listed
below:
2. $$2.6,6.6,4.8,5.4 , \quad 5.1 , \quad 4.5,6.9 , \quad 4.9,3.7,3.8$$ The department if natural resources is concerned that the mean PCB concentration for
fish from this lake exceeds 5 ppb.
a) What null and alternative hypotheses should the investigators use? In a few
sentences, justify your choice of the alternative hypothesis.
b) Using a graphic technique of your choice, show that the t-procedures are
appropriate to use with these data.
c) Using your hypotheses from part (a), carry out a hypothesis test using α= 0.05
and interpret the results.
d) In the context of this study, describe a Type I and a Type II error.

Accepted Answer

The answer of The department of natural resources classifies a...

Exam 12: Asking and Answering Questions About a Population Mean

In a few sentences, describe the difference between statistical and practical significance.

As $n$ increases, the mean of the sampling distribution of $\bar { x }$ gets closer to $\mu$ .

The $t$ confidence interval formula for estimating $\mu$ is appropriate when the population being sampled is approximately normally distributed.

A A random sample of size $n = 25$ is selected from a population with mean $\mu = 50$ and standard deviation $\sigma = 10$ . Determine the mean and standard deviation of the sampling distribution of $\bar { x }$ .

In a few sentences, describe the difference between statistical and practical significance.

A statistic is a characteristic of a population.

We say that the result of a hypothesis test is "statistically significant" when the P-value is less than or equal toα.

If the null hypothesis is not rejected, there is strong statistical evidence that the null hypothesis is true.

Exam 12: Asking and Answering Questions About a Population Mean

In a few sentences, describe the difference between statistical and practical significance.

As nnn increases, the mean of the sampling distribution of xˉ\bar { x }xˉ gets closer to μ\muμ .

The ttt confidence interval formula for estimating μ\muμ is appropriate when the population being sampled is approximately normally distributed.

A A random sample of size n=25n = 25n=25 is selected from a population with mean μ=50\mu = 50μ=50 and standard deviation σ=10\sigma = 10σ=10 . Determine the mean and standard deviation of the sampling distribution of xˉ\bar { x }xˉ .

In a few sentences, describe the difference between statistical and practical significance.

A statistic is a characteristic of a population.

We say that the result of a hypothesis test is "statistically significant" when the P-value is less than or equal toα.

If the null hypothesis is not rejected, there is strong statistical evidence that the null hypothesis is true.

As $n$ increases, the mean of the sampling distribution of $\bar { x }$ gets closer to $\mu$ .

The $t$ confidence interval formula for estimating $\mu$ is appropriate when the population being sampled is approximately normally distributed.

A A random sample of size $n = 25$ is selected from a population with mean $\mu = 50$ and standard deviation $\sigma = 10$ . Determine the mean and standard deviation of the sampling distribution of $\bar { x }$ .