Question 1

We have calculated a 95% confidence interval and would prefer for our next confidence interval to
Have a smaller margin of error without losing any confidence. In order to do this, we can
I. change the z value to a smaller number.
II. take a larger sample.
III. take a smaller sample.
A) I and III
B) I and II
C) III only
D) I only
E) II only

Accepted Answer

Taking a larger sample size reduces the margin of error while maintaining the same level of confidence.

Question 2

The manager of an orchard expects about 70% of his apples to exceed the weight requirement for
"Grade A" designation. At least how many apples must he sample to be 90% confident of
Estimating the true proportion within ±4%?
A) 89
B) 19
C) 23
D) 356
E) 505

Accepted Answer

The answer of The manager of an orchard expects about...

Question 3

Which is true about a 98% confidence interval for a population proportion based on a given
Sample?
I. We are 98% confident that other sample proportions will be in our interval.
II. There is a 98% chance that our interval contains the population proportion.
III. The interval is wider than a 95% confidence interval would be.
A) II only
B) I and II
C) I only
D) none of these
E) III only

Accepted Answer

A 98% confidence interval is wider than a 95% confidence interval because it provides more certainty that the interval contains the population proportion.

Question 4

We have calculated a confidence interval based upon a sample of n = 200. Now we want to get a Better estimate with a margin of error only one fifth as large. We need a new sample with
…
A) 450
B) 1000
C) 5000
D) 40

Accepted Answer

To reduce the margin of error to one fifth, the sample size must be increased by a factor of 25 (since the margin of error is inversely proportional to the square root of the sample size). Therefore, the new sample size should be 200 * 25 = 5000.

Question 5

Cereal A box of Raspberry Crunch cereal contains a mean of 13 ounces with a standard
deviation of 0.5 ounce. The distribution of the contents of cereal boxes is approximately
Normal. What is the probability that a case of 12 cereal boxes contains a total of more than
160 ounces?

Accepted Answer

The answer of Cereal A box of Raspberry Crunch cereal...

Question 6

Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than $97 \%$ good parts $\left( \mathrm { H } _ { 0 } : p = 0.97 \right.$ and $\left. \mathrm { H } _ { \mathrm { A } } : p > 0.97 \right)$. The test results in a $P$-value of $0.122$. Unknown to the manufacturer, the machine is actually producing $99 \%$ good parts. What probably happens as a result of the testing?
A) They correctly reject $\mathrm { H } _ { 0 }$.
B) They fail to reject $\mathrm { H } _ { 0 }$, making a Type I error.
C) They correctly fail to reject $\mathrm { H } _ { 0 }$.
D) They fail to reject $\mathrm { H } _ { 0 }$, making a Type II error.
E) They reject $\mathrm { H } _ { 0 }$, making a Type I error.

Accepted Answer

The P-value of 0.122 is greater than typical significance levels (e.g., 0.05), so they fail to reject $ H_0 $. Since the true proportion is 0.99, failing to reject $ H_0 $ is a Type II error.

Question 7

In the larger sample the proportion of people living in a home in which a language other
than English is spoken was 20.8%. The consultant decided this increase was statistically
significant. Now that the group is convinced the proportion has increased, why might they
still choose not to organize the campaign?

Accepted Answer

The answer of In the larger sample the proportion of...

Question 8

Not wanting to risk poor sales for a new soda flavor, a company decides to run one more taste test
On potential customers, this time requiring a higher approval rating than they had for earlier tests.
This higher standard of proof will increase
I. the risk of Type I error
II. the risk of Type II error
III. power
A) I and III
B) II only
C) III only
D) I only
E) I and II

Accepted Answer

Increasing the standard of proof (requiring a higher approval rating) decreases the risk of Type I error but increases the risk of Type II error, as it becomes harder to detect a true effect.

Question 9

Internet access A recent Gallup poll found that 28% of U.S. teens aged 13-17 have a
computer with Internet access in their rooms. The poll was based on a random sample of
1028 teens and reported a margin of error of $$\pm 3 \%$$ 
3%. What level of confidence did Gallup use
for this poll?

Accepted Answer

The answer of Internet access A recent Gallup poll found...

Question 10

Sleep Do more than 50% of U.S. adults feel they get enough sleep? According to Gallup's
December 2004 Lifestyle poll, 55% of U.S. adults said that that they get enough sleep. The
poll was based on a random sample of 1003 U.S. adults. Test an appropriate hypothesis
and state your conclusion in the context of the problem.

Accepted Answer

The answer of Sleep Do more than 50% of U.S....

Question 11

Which of the following is true about Type I and Type II errors?
I. Type I errors are always worse than Type II errors.
II. The severity of Type I and Type II errors depends on the situation being tested.
III. In any given situation, the higher the risk of Type I error, the lower the risk of Type II error.
A) I only
B) I and III
C) II only
D) III only
E) II and III

Accepted Answer

The severity of Type I and Type II errors depends on the context of the situation being tested, and there is a trade-off between the risks of Type I and Type II errors; reducing one typically increases the other.

Question 12

A certain population is strongly skewed to the right. We want to estimate its mean, so we will
Collect a sample. Which should be true if we use a large sample rather than a small one?
I. The distribution of our sample data will be closer to normal.
II. The sampling model of the sample means will be closer to normal.
III. The variability of the sample means will be greater.
A) II only
B) I only
C) II and III only
D) I and III only
E) III only

Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample means will be approximately normal if the sample size is large enough, regardless of the population's distribution. Hence, statement II is true. Statement I is incorrect because the distribution of the sample data itself does not become normal with a larger sample size. Statement III is incorrect because the variability of the sample means decreases with a larger sample size.

Question 13

Approval rating The President's job approval rating is always a hot topic. Your local paper
conducts a poll of 100 randomly selected adults to determine the President's job approval
rating. A CNN/USA Today/Gallup poll conducts a poll of 1010 randomly selected adults.
Which poll is more likely to report that the President's approval rating is below 50%,assuming that his actual approval rating is 54%? Explain.

Accepted Answer

The answer of Approval rating The President's job approval rating...

Question 14

A coffee house owner knows that customers pour different amounts of coffee into their cups. She Samples cups from 10 costumers she believes to be representative of the customers and weighs the Cups, finding a mean of 12.5 ounces and standard deviation of 0.5 ounces. Assuming these cups of Coffee can be considered a random sample of all cups of coffee which of the following formulas Gives a 95% confidence interval for the mean weight of all cups of coffee? 
A) $12.5 \pm 2.228 \left( \frac { 0.5 } { \sqrt { 9 } } \right)$
B) $12.5 \pm 2.262 \left( \frac { 0.5 } { \sqrt { 9 } } \right)$
C) $12.5 \pm 1.969 \left( \frac { 0.5 } { \sqrt { 10 } } \right)$
D) $12.5 \pm 2.262 \left( \frac { 0.5 } { \sqrt { 10 } } \right)$
E) $12.5 \pm 2.228 \left( \frac { 0.5 } { \sqrt { 10 } } \right\}$

Accepted Answer

The correct formula for a 95% confidence interval for the mean when using a t-distribution with a sample size of 10 is $ \bar{x} \pm t_{0.025, n-1} \left( \frac{s}{\sqrt{n}} \right) $. Here, $ \bar{x} = 12.5 $, $ s = 0.5 $, $ n = 10 $, and the t-value for 9 degrees of freedom at 95% confidence is approximately 2.262.

Question 15

A certain population is bimodal. We want to estimate its mean, so we will collect a sample. Which
Should be true if we use a large sample rather than a small one?
I. The distribution of our sample data will be more clearly bimodal.
II. The sampling distribution of the sample means will be approximately normal.
III. The variability of the sample means will be smaller.
A) I only
B) III only
C) II only
D) I, II, and III
E) II and III

Accepted Answer

The answer of A certain population is bimodal. We want...

Question 16

A consultant talked the group into gathering a larger sample. Will the power of the test
increase, decrease, or remain the same?

Accepted Answer

The answer of A consultant talked the group into gathering...

Question 17

Too much TV? A father is concerned that his teenage son is watching too much television
each day, since his son watches an average of 2 hours per day. His son says that his TV
habits are no different than those of his friends. Since this father has taken a stats class, he
knows that he can actually test to see whether or not his son is watching more TV than his
peers. The father collects a random sample of television watching times from boys at his
son's high school and gets the following data:
1.9 2.3 2.2 1.9 1.6 2.6 1.4 2.0 2.0 2.2
Is the father right? That is, is there evidence that other boys average less than 2 hours of
television per day? Conduct a hypothesis test, making sure to state your conclusions in the
context of the problem.

Accepted Answer

The answer of Too much TV? A father is concerned...

Question 18

A P-value indicates
A) the probability the null is true given the observed statistic.
B) the probability that the alternative hypothesis is true.
C) the probability of the observed statistic given that the null hypothesis is true.
D) the probability of the observed statistic given that the alternative hypothesis is true.
E) the probability that the null hypothesis is true.

Accepted Answer

The P-value is the probability of observing the data, or something more extreme, assuming that the null hypothesis is true.

Question 19

A statistics professor wants to see if more than 80% of her students enjoyed taking her class. At the End of the term, she takes a random sample of students from her large class and asks, in an Anonymous survey, if the students enjoyed taking her class. Which set of hypotheses should she Test? A) $\mathrm { H } _ { 0 } : p > 0.80$ $\mathrm { H } _ { \mathrm { A } } : p = 0.80$ B) $\mathrm { H } _ { 0 } : p < 0.80$ $\mathrm { H } _ { \mathrm { A } } : p > 0.80$ C) $\mathrm { H } _ { 0 } : p = 0.80$ $\mathrm { H } _ { \mathrm { A } } : p < 0.80$ D) $\mathrm { H } _ { 0 } : p = 0.80$ $\mathrm { H } _ { \mathrm { A } } : p > 0.80$ E) $\mathrm { H } _ { 0 } : p < 0.80$ \ (\mathrm { H } _ { \mathrm { A } } : p \neq 0.80\)

Accepted Answer

The null hypothesis ($H_0$) should state that the proportion is equal to 0.80, and the alternative hypothesis ($H_A$) should state that the proportion is greater than 0.80, as the professor wants to test if more than 80% of students enjoyed the class.

Question 20

We have calculated a confidence interval based on a sample of size n = 100. Now we want to get a
Better estimate with a margin of error that is only one-fourth as large. How large does our new
Sample need to be?
A) 50
B) 400
C) 200
D) 1600
E) 25

Accepted Answer

The answer of We have calculated a confidence interval based...

Quiz 8: Regression, Associations, and Predictive Modeling

We have calculated a 95% confidence interval and would prefer for our next confidence interval to Have a smaller margin of error without losing any confidence. In order to do this, we can I. change the z value to a smaller number. II. take a larger sample. III. take a smaller sample.

The manager of an orchard expects about 70% of his apples to exceed the weight requirement for "Grade A" designation. At least how many apples must he sample to be 90% confident of Estimating the true proportion within ±4%?

We have calculated a confidence interval based upon a sample of n = 200. Now we want to get a Better estimate with a margin of error only one fifth as large. We need a new sample with …

Cereal A box of Raspberry Crunch cereal contains a mean of 13 ounces with a standard deviation of 0.5 ounce. The distribution of the contents of cereal boxes is approximately Normal. What is the probability that a case of 12 cereal boxes contains a total of more than 160 ounces?

Internet access A recent Gallup poll found that 28% of U.S. teens aged 13-17 have a computer with Internet access in their rooms. The poll was based on a random sample of 1028 teens and reported a margin of error of $\pm 3 \%$ 3%. What level of confidence did Gallup use for this poll?

A consultant talked the group into gathering a larger sample. Will the power of the test increase, decrease, or remain the same?

A P-value indicates

A statistics professor wants to see if more than 80% of her students enjoyed taking her class. At the End of the term, she takes a random sample of students from her large class and asks, in an Anonymous survey, if the students enjoyed taking her class. Which set of hypotheses should she Test?

We have calculated a confidence interval based on a sample of size n = 100. Now we want to get a Better estimate with a margin of error that is only one-fourth as large. How large does our new Sample need to be?