Question 1

For the given data value, find the standard score and the percentile.
-A data value $1.3$ standard deviations above the mean.

Accepted Answer

A)  $z = 1.3$; percentile $= 2.2$ 
B)  $z = 0.13$; percentile $= 55.96$ 
C)  $z = - 1.3$; percentile $= 9.68$ 
D)  $z = 1.3$; percentile $= 90.32$ 
A)  $z = 1.3$; percentile $= 2.2$ 
B)  $z = 0.13$; percentile $= 55.96$ 
C)  $z = - 1.3$; percentile $= 9.68$ 
D)  $z = 1.3$; percentile $= 90.32$

Question 2

Solve the problem.
-The grades are given for a student for a particular semester. Use weighted means to find the grade point average. Assume the grade point values ar $\mathrm { A } = 4 , \mathrm {~B} = 3 , \mathrm { C } = 2 , \mathrm { D } = 1 , \text { and } \mathrm { F } = 0$ und your Answer to the nearest tenth when necessary. 
$\begin{array}{cc}
\text { Grade } & \text { Credit Hours } \
\hline \text { A } & 3 \
\text { D } & 1 \
\text { D } & 2 \
\text { F } & 2 \
\text { D } & 3
\end{array}$

Accepted Answer

A)  11 
B)  $1.6$ 
C)  $1.4$ 
D)  $2.2$ 
A)  11 
B)  $1.6$ 
C)  $1.4$ 
D)  $2.2$

Question 3

Provide an appropriate response.
-In essence, the standard deviation indicates how far, on average, the observations are from
the mean. Do you think that for the data set below the standard deviation will give a good
indication of the typical deviation from the mean? $2,3,4,4,5,5,6,6,100$ What drawback of the standard deviation is illustrated by this example?

Accepted Answer

No, the standard deviation is 31.9. This

Question 4

Use the 68-95-99.7 rule to solve the problem.
-Assume that a distribution has a mean of 26 and a standard deviation of 7. What percentage of the values in the distribution do we expect to fall between 26 and 40?

Accepted Answer

A) 47.5% 
B) 25% 
C) 5% 
D) 95% 
A) 47.5% 
B) 25% 
C) 5% 
D) 95%

Question 5

Answer the question.
-Tell which of the following distributions would have the least variation.

Accepted Answer

A) Number of children for women in Kenya 
B) Number of children for women in Portland, Oregon 
C) Number of children for women in India 
D) Number of children for women in Haiti 
A) Number of children for women in Kenya 
B) Number of children for women in Portland, Oregon 
C) Number of children for women in India 
D) Number of children for women in Haiti

Question 6

Provide an appropriate response.
-Toni is conducting a hypothesis test concerning a population proportion. The hypotheses are as follows.
Null hypothesis: population proportion $= 0.2$
Alternative hypothesis.: population proportion $> 0.2$
She selects a sample and finds that the sample proportion is $0.21$. She then does some calculations and is able to make the following statement:
If the population proportion were $0.2$, the chance that the sample proportion would have come out as big as $0.21$ or bigger is $0.4$. Which of the following is a reasonable conclusion?

Accepted Answer

A)  Accept the alternative hypothesis. The sample provides evidence to support the alternative hypothesis. 
B)  Do not reject the null hypothesis. The sample provides no evidence against the null hypothesis. 
C)  Accept the null hypothesis. The sample provides no evidence against the alternative hypothesis. 
D)  Accept the null hypothesis. The sample provides evidence to support the null hypothesis. 
A)  Accept the alternative hypothesis. The sample provides evidence to support the alternative hypothesis. 
B)  Do not reject the null hypothesis. The sample provides no evidence against the null hypothesis. 
C)  Accept the null hypothesis. The sample provides no evidence against the alternative hypothesis. 
D)  Accept the null hypothesis. The sample provides evidence to support the null hypothesis.

Question 7

A hypothesis test is to be performed. State the null and alternative hypotheses.
-A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $\$ 1200$. They suspect that the average fee charged by one particular clinic for this procedure is higher than $\$ 1200$. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct.

Accepted Answer

A)  Null hypothesis: mean fee $= \$ 1200$ 
B)  Null hypothesis: mean fee $> \$ 1200$
Alternative hypothesis: mean fee $> \$ 1200$
Alternative hypothesis: mean fee $= \$ 1200$ 
C)  Null hypothesis: mean fee $= \$ 1200$
Alternative hypothesis: mean fee $\geq \$ 1200$ 
D)  Null hypothesis: mean fee $ \$ 1200$ 
A)  Null hypothesis: mean fee $= \$ 1200$ 
B)  Null hypothesis: mean fee $> \$ 1200$
Alternative hypothesis: mean fee $> \$ 1200$
Alternative hypothesis: mean fee $= \$ 1200$ 
C)  Null hypothesis: mean fee $= \$ 1200$
Alternative hypothesis: mean fee $\geq \$ 1200$ 
D)  Null hypothesis: mean fee $ \$ 1200$

Question 8

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explainyour thinking.
-The table below provides a frequency distribution for the winner of the Davis Cup during
the period 1977-1994. Winner of
$\begin{array}{lc}
\text { Davis Cup } & \text { Frequency } \
\hline \text { United States } & 6 \
\text { Germany } & 3 \
\text { Czechoslovakia } & 1 \
\text { Australia } & 3 \
\text { France } & 1 \
\text { Sweden } & 4
\end{array}$

Which measure of center, the mean, the median, or the mode is most appropriate here? Why?

Accepted Answer

The mode. The data (winning co

Question 9

A hypothesis test is to be performed. State the null and alternative hypotheses.
-A consumer group believes that the proportion of defects among computers produced by one manufacturer is greater than the $2 \%$ claimed by the company.

Accepted Answer

A)  Null hypothesis: proportion of defectives $= 2 \%$
Alternative hypothesis: proportion of defectives $> 2 \%$ 
B)  Null hypothesis: proportion of defectives $= 2 \%$
Alternative hypothesis: proportion of defectives $\geq 2 \%$ 
C)  Null hypothesis: proportion of defectives $> 2 \%$
Alternative hypothesis: proportion of defectives $= 2 \%$ 
D)  Null hypothesis: proportion of defectives $ 2 \%$ 
A)  Null hypothesis: proportion of defectives $= 2 \%$
Alternative hypothesis: proportion of defectives $> 2 \%$ 
B)  Null hypothesis: proportion of defectives $= 2 \%$
Alternative hypothesis: proportion of defectives $\geq 2 \%$ 
C)  Null hypothesis: proportion of defectives $> 2 \%$
Alternative hypothesis: proportion of defectives $= 2 \%$ 
D)  Null hypothesis: proportion of defectives $ 2 \%$

Question 10

State whether you would expect the data set to be normally distributed.
-The amount of property taxes paid by homeowners

Accepted Answer

A) Normal 
B) Not normal 
A) Normal 
B) Not normal

Question 11

Find the mode(s)for the given sample data.
-The weights (in ounces) of 14 different apples are shown below.
$\begin{array} { l l l l l l l } 4.6 & 4.8 & 4.9 & 5.2 & 4.1 & 4.6 & 4.8 \end{array}$
$\begin{array} { l l l l l l l } 4.7 & 5.0 & 5.2 & 4.6 & 4.7 & 5.2 & 6.5 \end{array}$

Accepted Answer

A)  $4.90$ 
B)  $4.6$ 
C)  $4.6,5.2$ 
D)  None 
A)  $4.90$ 
B)  $4.6$ 
C)  $4.6,5.2$ 
D)  None

Question 12

Explanation:
-The amount of coffee which a filling machine puts into "4 ounce jars"

Accepted Answer

A) Not normal 
B) Normal 
A) Not normal 
B) Normal

Question 13

Solve the problem.
-Find the mean for the given sample data. Round your answer to the nearest tenth if necessary. $20,18,20,20,12$

Accepted Answer

A)  17 
B)  18 
C)  20 
D)  $22.5$ 
A)  17 
B)  18 
C)  20 
D)  $22.5$

Question 14

Find a 95% confidence interval for the true population proportion.
-In a survey of 114 adults, 24% said that they had tried acupuncture at some point in their lives.

Accepted Answer

A) 23.1% to 24.9% 
B) 23.9% to 24.1% 
C) 19.3% to 28.7% 
D) 14.6% to 33.4% 
A) 23.1% to 24.9% 
B) 23.9% to 24.1% 
C) 19.3% to 28.7% 
D) 14.6% to 33.4%

Question 15

Provide an appropriate response.
-A data set consists of 9 values which are not all the same. Which of the following is possible?

Accepted Answer

A) The mode is equal to the largest value. 
B) The mean is equal to the largest value. 
C) The median is equal to the largest value. 
D) None of the above is possible. 
A) The mode is equal to the largest value. 
B) The mean is equal to the largest value. 
C) The median is equal to the largest value. 
D) None of the above is possible.

Question 16

Provide an appropriate response.
-A data set consists of 9 values which are all different. Which of the following is possible?

Accepted Answer

A) The median is equal to the second smallest value. 
B) The mean is equal to the second smallest value. 
C) The mode is equal to the second smallest value. 
D) None of the above is possible. 
A) The median is equal to the second smallest value. 
B) The mean is equal to the second smallest value. 
C) The mode is equal to the second smallest value. 
D) None of the above is possible.

Question 17

For the given data value, find the standard score and the percentile.
-A data value 0.6 standard deviations above the mean.

Accepted Answer

A)  $z = 0.06$; percentile $= 51.99$ 
B)  $\mathrm { z } = 0.6$; percentile $= 72.57$ 
C)  $\mathrm { z } = 0.6$; percentile $= 2.5$ 
D)  $\mathrm { z } = - 0.6$; percentile $= 27.43$ 
A)  $z = 0.06$; percentile $= 51.99$ 
B)  $\mathrm { z } = 0.6$; percentile $= 72.57$ 
C)  $\mathrm { z } = 0.6$; percentile $= 2.5$ 
D)  $\mathrm { z } = - 0.6$; percentile $= 27.43$

Question 18

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the givensituation.
-During one flu epidemic the proportion of adults nationwide who have come down with the flu is $8 \%$. The manufacturer of a flu vaccine claims that those who have been vaccinated are less likely to catch the flu.
The hypotheses are as follows:
Null hypothesis: proportion of those vaccinated catching the flu $= 8 \%$
Alternative hypothesis: proportion of those vaccinated catching the flu $< 8 \%$

Accepted Answer

A)  Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is not equal to $8 \%$
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is equal to $8 \%$. 
B)  Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than $8 \%$
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is less than $8 \%$. 
C)  Rejecting the null hypothesis means there is insufficient evidence that the proportion of those vaccinated catching the flu is equal to $8 \%$
Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to $8 \%$. 
D)  Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than $8 \%$
Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to $8 \%$. 
A)  Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is not equal to $8 \%$
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is equal to $8 \%$. 
B)  Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than $8 \%$
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is less than $8 \%$. 
C)  Rejecting the null hypothesis means there is insufficient evidence that the proportion of those vaccinated catching the flu is equal to $8 \%$
Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to $8 \%$. 
D)  Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than $8 \%$
Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to $8 \%$.

Question 19

Use the 68-95-99.7 rule to solve the problem.
-The amount of Jen's monthly phone bill is normally distributed with a mean of $70 and a standard deviation of $9. What percentage of her phone bills are between $43 and $97?

Accepted Answer

A) 68% 
B) 95% 
C) 99.9% 
D) 99.7% 
A) 68% 
B) 95% 
C) 99.9% 
D) 99.7%

Question 20

Find the margin of error for the survey results described.
-During the questioning of 82 potential jury members, 33% said that they had already formed an opinion as to the guilt of the defendant.
Give your answer as a percentage to one decimal place.

Accepted Answer

A) 1.2% 
B) 22.1% 
C) 5.5% 
D) 11.0% 
A) 1.2% 
B) 22.1% 
C) 5.5% 
D) 11.0%

For the given data value, find the standard score and the percentile. -A data value $1.3$ standard deviations above the mean.

Use the 68-95-99.7 rule to solve the problem. -Assume that a distribution has a mean of 26 and a standard deviation of 7. What percentage of the values in the distribution do we expect to fall between 26 and 40?

Answer the question. -Tell which of the following distributions would have the least variation.

A hypothesis test is to be performed. State the null and alternative hypotheses. -A consumer group believes that the proportion of defects among computers produced by one manufacturer is greater than the $2 \%$ claimed by the company.

State whether you would expect the data set to be normally distributed. -The amount of property taxes paid by homeowners

Find the mode(s)for the given sample data. -The weights (in ounces) of 14 different apples are shown below. 4.6 4.8 4.9 5.2 4.1 4.6 4.8 4.7 5.0 5.2 4.6 4.7 5.2 6.5

Explanation: -The amount of coffee which a filling machine puts into "4 ounce jars"

Solve the problem. -Find the mean for the given sample data. Round your answer to the nearest tenth if necessary. $20,18,20,20,12$

Find a 95% confidence interval for the true population proportion. -In a survey of 114 adults, 24% said that they had tried acupuncture at some point in their lives.

Provide an appropriate response. -A data set consists of 9 values which are not all the same. Which of the following is possible?

Provide an appropriate response. -A data set consists of 9 values which are all different. Which of the following is possible?

For the given data value, find the standard score and the percentile. -A data value 0.6 standard deviations above the mean.

Use the 68-95-99.7 rule to solve the problem. -The amount of Jen's monthly phone bill is normally distributed with a mean of $70 and a standard deviation of $9. What percentage of her phone bills are between $43 and $97?

Find the margin of error for the survey results described. -During the questioning of 82 potential jury members, 33% said that they had already formed an opinion as to the guilt of the defendant. Give your answer as a percentage to one decimal place.

Thinking Critically

Approaches to Problem Solving

Numbers in the Real World

Managing Money

Statistical Reasoning

Probability: Living With the Odds

Exponential Astonishment

Modeling Our World

Modeling With Geometry

Mathematics and the Arts

Filters

Exam 6: Putting Statistics to Work

For the given data value, find the standard score and the percentile. -A data value 1.31.31.3 standard deviations above the mean.