Question 1

The symbol for the sample proportion is .

Accepted Answer

$\hat { p }$

Question 2

A college admissions officer takes a simple random sample of 90 entering freshmen and computes their mean mathematics SAT score to be 436 . Assume the population standard deviation is $\sigma = 101$.

Based on a $99 \%$ confidence interval for the mean mathematics SAT score, is it likely that the mean mathematics SAT score for entering freshmen class is greater than 460 ? (Hint: you should first construct the $99 \%$ confidence interval for the mean mathematics SAT score.)

Accepted Answer

A)  The likelihood cannot be determined. 
B)  Yes 
C)  No 
A)  The likelihood cannot be determined. 
B)  Yes 
C)  No B

Question 3

The three confidence intervals below were constructed from the same sample. One of them was computed at a confidence level of 90%, another at a confidence level of 95%, and another at a
Confidence level of 98%.
Which is the confidence level at 98%?

Accepted Answer

A)  $31.3 < \mu < 40.7$ 
B)  cannot be determined 
C)  $30.3 < \mu < 41.7$ 
D)  $29.3 < \mu < 42.7$ 
A)  $31.3 < \mu < 40.7$ 
B)  cannot be determined 
C)  $30.3 < \mu < 41.7$ 
D)  $29.3 < \mu < 42.7$ D

Question 4

$$\text { Find } t _ { \alpha / 2 } \text { when } n = 12 \text { for the } 95 \% \text { confidence interval for the mean. }$$

Accepted Answer

A)  2.20 
B)  1.52 
C)  1.80 
D)  2.92 
A)  2.20 
B)  1.52 
C)  1.80 
D)  2.92

Question 5

The following MINITAB output presents a confidence interval for a population mean.
$\begin{array}{crrccc}
\hline \text { Variable } & \mathrm{N} & \text { Mean } & \text { StDev } & \text { SE Mean } & 99 \% \mathrm{CI} \
\mathrm{x} & 28 & 108.1268 & 30.4888 & 5.7618 & (92.161,124.093) \
\hline
\end{array}$
Use the information in the output to construct a $98 \%$ confidence interval.

Accepted Answer

A)  (92.161, 124.093) 
B)  (105.235, 111.018) 
C)  (93.878, 122.376) 
D)  (105.546, 110.707) 
A)  (92.161, 124.093) 
B)  (105.235, 111.018) 
C)  (93.878, 122.376) 
D)  (105.546, 110.707)

Question 6

The following display from a TI-84 Plus calculator presents a $95 \%$ confidence interval.

Fill in the blanks: We are _____confident that the population mean is between______ _ and

Accepted Answer

A)  95%, 29.856, 39.608 
B)  5%, 0, 34.732 
C)  95%, 0, 34.732 
D)  5%, 29.856, 39.608 
A)  95%, 29.856, 39.608 
B)  5%, 0, 34.732 
C)  95%, 0, 34.732 
D)  5%, 29.856, 39.608

Question 7

$$\text { The term } z _ { \alpha / 2 } \left( \frac { \sigma } { \sqrt { n } } \right) \text { describes the }$$_______

Accepted Answer

A)  confidence interval 
B)  maximum error of estimate 
C)  unbiased estimator 
D)  interval estimate 
A)  confidence interval 
B)  maximum error of estimate 
C)  unbiased estimator 
D)  interval estimate

Question 8

The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this proportion is within
3 percentage points of the true proportion. How large a sample is necessary?

Accepted Answer

A)  683 
B)  484 
C)  966 
D)  1183 
A)  683 
B)  484 
C)  966 
D)  1183

Question 9

A researcher conducted a study of the access speed of 45 hard drives and concluded that his maximum error of estimate was 24. If he were to conduct a second study to reduce
The maximum error of estimate to 6, about how many hard drives should he include in his
New sample?

Accepted Answer

A)  720 
B)  90 
C)  45 
D)  180 
A)  720 
B)  90 
C)  45 
D)  180

Question 10

A study of 40 white mice showed that their average weight was 3.20 ounces. The standard deviation of the population is 0.8 ounces. Which of the following is the 80%
Confidence interval for the mean weight per white mouse?

Accepted Answer

A)  $3.04 < \mu < 3.36$ 
B)  $2.88 < \mu < 3.52$ 
C)  $3.12 < \mu < 3.28$ 
D)  $3.09 < \mu < 3.31$ 
A)  $3.04 < \mu < 3.36$ 
B)  $2.88 < \mu < 3.52$ 
C)  $3.12 < \mu < 3.28$ 
D)  $3.09 < \mu < 3.31$

Question 11

The following display from a TI-84 Plus calculator presents a $99 \%$ confidence interval for proportion.
 
 a Fill in the blanks: We are ________ confident that the population mean is between _______ and
_______.

Accepted Answer

A)  99%, 0.157092, 0.495330 
B)  99%, 0, 0.326211 
C)  1%, 0.157092, 0.495330 
D)  1%, 0, 0.326211 
A)  99%, 0.157092, 0.495330 
B)  99%, 0, 0.326211 
C)  1%, 0.157092, 0.495330 
D)  1%, 0, 0.326211

Question 12

A sample of size $n = 21$ is drawn from a normal population. Find the critical value needed to construct a $90 \%$ confidence interval.

Accepted Answer

A)  1.721 
B)  1.645 
C)  1.725 
D)  1.325 
A)  1.721 
B)  1.645 
C)  1.725 
D)  1.325

Question 13

In a survey of 445 registered voters, 131 of them wished to see Mayor Waffleskate lose her next election. The Waffleskate campaign claims that no more than 30% of registered
Voters wish to see her defeated. Does the 98% confidence interval for the proportion
Support this claim? (Hint: you should first construct the 98% confidence interval for the
Proportion of registered voters who whish to see Waffleskate defeated.)
(0)244, 0.345)

Accepted Answer

A)  Yes 
B)  No 
C)  The reasonableness of the claim cannot be determined. 
A)  Yes 
B)  No 
C)  The reasonableness of the claim cannot be determined.

Question 14

A report states that 42% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to
Within 4% with 95% confidence?

Accepted Answer

A)  293 
B)  585 
C)  1170 
D)  147 
A)  293 
B)  585 
C)  1170 
D)  147

Question 15

The $t$-distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed.

Accepted Answer

A) True 
 B)False

Question 16

Construct a $99 \%$ confidence interval for the population standard deviation $\sigma$ if a sample of size 11 has standard deviation $s = 15$.

Accepted Answer

A)  $9.45 < \sigma < 32.31$ 
B)  $9.17 < \sigma < 29.40$ 
C)  $9.85 < \sigma < 29.66$ 
D)  $9.62 < \sigma < 30.83$ 
A)  $9.45 < \sigma < 32.31$ 
B)  $9.17 < \sigma < 29.40$ 
C)  $9.85 < \sigma < 29.66$ 
D)  $9.62 < \sigma < 30.83$

Question 17

A sample of size $n = 56$ is drawn from a population whose standard deviation is Find the margin of error for a $95 \%$ confidence interval for $\mu$.

Accepted Answer

A)  0.60 
B)  3.26 
C)  0.56 
D)  1.18 
A)  0.60 
B)  3.26 
C)  0.56 
D)  1.18

Question 18

A study of 65 bolts of carpet showed that their average length was $74.2$ yards. The standard deviation of the population is $3.6$ yards. Which of the following is the $98 \%$ confidence interval for the mean length per bolt of carpet?

Accepted Answer

A)  $73.2 < \mu < 75.2$ 
B)  $72.1 < \mu < 76.3$ 
C)  $73.7 < \mu < 74.7$ 
D)  $73.3 < \mu < 75.1$ 
A)  $73.2 < \mu < 75.2$ 
B)  $72.1 < \mu < 76.3$ 
C)  $73.7 < \mu < 74.7$ 
D)  $73.3 < \mu < 75.1$

Question 19

The average number of mosquitos caught in 64 mosquito traps in a particular
environment was 700 per trap. The standard deviation of mosquitos caught in the
entire population of traps is 100 mosquitos. What is the 99% confidence interval
for the true mean number of mosquitos caught in all mosquito traps?

Accepted Answer

The answer of The average number of mosquitos caught in...

Question 20

Estimate the standard deviation in calories for these randomly selected standard-size candy bars with 95% confidence. (The number of calories is listed for each.) Assume the variable is
Normally distributed.
218 219 212 225 271 266 246
211 238 250 281 227 278 260

Accepted Answer

A)  $328.266 < \sigma ^ { 2 } < 1621.082$
$18.1 < \sigma < 40.3$ 
B)  $14.145 < \sigma ^ { 2 } < 69.853$
$3.8 < \sigma < 8.4$ 
C)  $13.135 < \sigma ^ { 2 } < 64.863$
$3.6 < \sigma < 8.1$ 
D)  $353.518 < \sigma ^ { 2 } < 1745.781$
$18.8 < \sigma < 41.8$ 
A)  $328.266 < \sigma ^ { 2 } < 1621.082$
$18.1 < \sigma < 40.3$ 
B)  $14.145 < \sigma ^ { 2 } < 69.853$
$3.8 < \sigma < 8.4$ 
C)  $13.135 < \sigma ^ { 2 } < 64.863$
$3.6 < \sigma < 8.1$ 
D)  $353.518 < \sigma ^ { 2 } < 1745.781$
$18.8 < \sigma < 41.8$

The symbol for the sample proportion is .

The three confidence intervals below were constructed from the same sample. One of them was computed at a confidence level of 90%, another at a confidence level of 95%, and another at a Confidence level of 98%. Which is the confidence level at 98%?

$\text { Find } t _ { \alpha / 2 } \text { when } n = 12 \text { for the } 95 \% \text { confidence interval for the mean. }$

The following MINITAB output presents a confidence interval for a population mean. Variable Mean StDev SE Mean 99\% 28 108.1268 30.4888 5.7618 (92.161,124.093) Use the information in the output to construct a $98 \%$ confidence interval.

$\text { The term } z _ { \alpha / 2 } \left( \frac { \sigma } { \sqrt { n } } \right) \text { describes the }$ _______

The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this proportion is within 3 percentage points of the true proportion. How large a sample is necessary?

A researcher conducted a study of the access speed of 45 hard drives and concluded that his maximum error of estimate was 24. If he were to conduct a second study to reduce The maximum error of estimate to 6, about how many hard drives should he include in his New sample?

A study of 40 white mice showed that their average weight was 3.20 ounces. The standard deviation of the population is 0.8 ounces. Which of the following is the 80% Confidence interval for the mean weight per white mouse?

A sample of size $n = 21$ is drawn from a normal population. Find the critical value needed to construct a $90 \%$ confidence interval.

A report states that 42% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to Within 4% with 95% confidence?

The $t$ -distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed.

Construct a $99 \%$ confidence interval for the population standard deviation $\sigma$ if a sample of size 11 has standard deviation $s = 15$ .

A sample of size $n = 56$ is drawn from a population whose standard deviation is Find the margin of error for a $95 \%$ confidence interval for $\mu$ .

A study of 65 bolts of carpet showed that their average length was $74.2$ yards. The standard deviation of the population is $3.6$ yards. Which of the following is the $98 \%$ confidence interval for the mean length per bolt of carpet?

Estimate the standard deviation in calories for these randomly selected standard-size candy bars with 95% confidence. (The number of calories is listed for each.) Assume the variable is Normally distributed. 218 219 212 225 271 266 246 211 238 250 281 227 278 260

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Probability and Counting Rules

Discrete Probability Distributions

The Normal Distribution

Hypothesis Testing

Testing the Difference Between Two Means, Two Variances, and Two Proportions

Correlation and Regression

Other Chi-Square Tests

Analysis of Variance

Nonparametric Statistics

Sampling and Simulation

Filters

Exam 7: Confidence Intervals and Sample Size

The symbol for the sample proportion is .

The three confidence intervals below were constructed from the same sample. One of them was computed at a confidence level of 90%, another at a confidence level of 95%, and another at a Confidence level of 98%. Which is the confidence level at 98%?

Find tα/2 when n=12 for the 95% confidence interval for the mean. \text { Find } t _ { \alpha / 2 } \text { when } n = 12 \text { for the } 95 \% \text { confidence interval for the mean. } Find tα/2​ when n=12 for the 95% confidence interval for the mean.

The following MINITAB output presents a confidence interval for a population mean. Variable Mean StDev SE Mean 99\% 28 108.1268 30.4888 5.7618 (92.161,124.093) Use the information in the output to construct a 98%98 \%98% confidence interval.

The following display from a TI-84 Plus calculator presents a 95%95 \%95% confidence interval. Fill in the blanks: We are _____confident that the population mean is between______ _ and

The term zα/2(σn) describes the \text { The term } z _ { \alpha / 2 } \left( \frac { \sigma } { \sqrt { n } } \right) \text { describes the } The term zα/2​(n​σ​) describes the _______

The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this proportion is within 3 percentage points of the true proportion. How large a sample is necessary?

A researcher conducted a study of the access speed of 45 hard drives and concluded that his maximum error of estimate was 24. If he were to conduct a second study to reduce The maximum error of estimate to 6, about how many hard drives should he include in his New sample?

A study of 40 white mice showed that their average weight was 3.20 ounces. The standard deviation of the population is 0.8 ounces. Which of the following is the 80% Confidence interval for the mean weight per white mouse?

The following display from a TI-84 Plus calculator presents a 99%99 \%99% confidence interval for proportion. a Fill in the blanks: We are ________ confident that the population mean is between _______ and _______.

A sample of size n=21n = 21n=21 is drawn from a normal population. Find the critical value needed to construct a 90%90 \%90% confidence interval.

A report states that 42% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to Within 4% with 95% confidence?

The ttt -distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed.

Construct a 99%99 \%99% confidence interval for the population standard deviation σ\sigmaσ if a sample of size 11 has standard deviation s=15s = 15s=15 .

A sample of size n=56n = 56n=56 is drawn from a population whose standard deviation is Find the margin of error for a 95%95 \%95% confidence interval for μ\muμ .

A study of 65 bolts of carpet showed that their average length was 74.274.274.2 yards. The standard deviation of the population is 3.63.63.6 yards. Which of the following is the 98%98 \%98% confidence interval for the mean length per bolt of carpet?

Estimate the standard deviation in calories for these randomly selected standard-size candy bars with 95% confidence. (The number of calories is listed for each.) Assume the variable is Normally distributed. 218 219 212 225 271 266 246 211 238 250 281 227 278 260

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Probability and Counting Rules

Discrete Probability Distributions

The Normal Distribution

Hypothesis Testing

Testing the Difference Between Two Means, Two Variances, and Two Proportions

Correlation and Regression

Other Chi-Square Tests

Analysis of Variance

Nonparametric Statistics

Sampling and Simulation

Filters

$\text { Find } t _ { \alpha / 2 } \text { when } n = 12 \text { for the } 95 \% \text { confidence interval for the mean. }$

The following MINITAB output presents a confidence interval for a population mean. Variable Mean StDev SE Mean 99\% 28 108.1268 30.4888 5.7618 (92.161,124.093) Use the information in the output to construct a $98 \%$ confidence interval.

$\text { The term } z _ { \alpha / 2 } \left( \frac { \sigma } { \sqrt { n } } \right) \text { describes the }$ _______

A sample of size $n = 21$ is drawn from a normal population. Find the critical value needed to construct a $90 \%$ confidence interval.

The $t$ -distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed.

Construct a $99 \%$ confidence interval for the population standard deviation $\sigma$ if a sample of size 11 has standard deviation $s = 15$ .

A sample of size $n = 56$ is drawn from a population whose standard deviation is Find the margin of error for a $95 \%$ confidence interval for $\mu$ .

A study of 65 bolts of carpet showed that their average length was $74.2$ yards. The standard deviation of the population is $3.6$ yards. Which of the following is the $98 \%$ confidence interval for the mean length per bolt of carpet?