Question 1

What is the confidence coefficient in a 95% confidence interval for $\mu$ ?

Accepted Answer

A)  .95 
B)  .025 
C)  .05 
D)  .475 
A)  .95 
B)  .025 
C)  .05 
D)  .475 A

Question 2

When the sample size is small, confidence intervals for a population proportion are more reliable  when the population proportion p is near 0 or 1.

Accepted Answer

A) True 
 B)False  False

Question 3

The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, $\bar { x } = 19.8$ and $s ^ { 2 } = 4$. If the director wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with $90 \%$ reliability, what is the minimum sample size she should use?

Accepted Answer

A)  7 
B)  27 
C)  44 
D)  11 
A)  7 
B)  27 
C)  44 
D)  11 D

Question 4

The Central Limit Theorem guarantees an approximately normal sampling distribution for the  sample mean for large sample sizes, so no knowledge about the distribution of the population is necessary for the corresponding interval to be valid.

Accepted Answer

A) True 
 B)False

Question 5

The mean systolic blood pressure for a random sample of 28 women aged 18-24 is 114.9 mm Hg and the standard deviation is 13.1 mm Hg. Construct a 90% confidence interval for the standard deviation ?, of the systolic blood pressures of all women aged 18-24. Round to the nearest hundredth when necessary.

Accepted Answer

A)  (10.22, 18.34) 
B)  (10.75, 16.94) 
C)  (11.23, 15.99) 
D)  (10.59, 16.54) 
A)  (10.22, 18.34) 
B)  (10.75, 16.94) 
C)  (11.23, 15.99) 
D)  (10.59, 16.54)

Question 6

The registrar's office at State University would like to determine a 95% confidence interval for the mean commute time of its students. A member of the staff randomly chooses a parking lot and surveys the first 125 students who park in the chosen lot on a given day. The confidence interval is

Accepted Answer

A)  not meaningful because of the lack of random sampling. 
B)  not meaningful because the sampling distribution of the sample mean is not normal. 
C)  meaningful because the sample is representative of the population. 
D)  meaningful because the sample size exceeds 30 and the Central Limit Theorem ensures normality of the sampling distribution of the sample mean. 
A)  not meaningful because of the lack of random sampling. 
B)  not meaningful because the sampling distribution of the sample mean is not normal. 
C)  meaningful because the sample is representative of the population. 
D)  meaningful because the sample size exceeds 30 and the Central Limit Theorem ensures normality of the sampling distribution of the sample mean.

Question 7

Explain what the phrase 95% confident means when we interpret a 95% confidence interval for µ.

Accepted Answer

A)  95% of the observations in the population fall within the bounds of the calculated interval. 
B)  In repeated sampling, 95% of similarly constructed intervals contain the value of the population mean. 
C)  95% of similarly constructed intervals would contain the value of the sampled mean. 
D)  The probability that the sample mean falls in the calculated interval is 0.95. 
A)  95% of the observations in the population fall within the bounds of the calculated interval. 
B)  In repeated sampling, 95% of similarly constructed intervals contain the value of the population mean. 
C)  95% of similarly constructed intervals would contain the value of the sampled mean. 
D)  The probability that the sample mean falls in the calculated interval is 0.95.

Question 8

Let $t _ { 0 }$ be a particular value of $t$. Find a value of $t _ { 0 }$ such that $P \left( t \leq t _ { 0 } \right.$ or $\left. t \geq t _ { 0 } \right) = .1$ where $\mathrm { df } =$ 14 .

Accepted Answer

The answer of Let $t _ { 0 }$ be...

Question 9

Fifteen SmartCars were randomly selected and the highway mileage of each was noted. The analysis yielded a mean of 47 miles per gallon and a standard deviation of 5 miles per gallon.
Which of the following would represent a 90% confidence interval for the average highway
Mileage of all SmartCars?

Accepted Answer

A)  $47 \pm 1.753 \frac { 5 } { \sqrt { 15 } }$ 
B)  $47 \pm 1.761 \frac { 5 } { \sqrt { 15 } }$ 
C)  $47 \pm 1.645 \frac { 5 } { \sqrt { 15 } }$ 
D)  $47 \pm 1.345 \frac { 5 } { \sqrt { 15 } }$ 
A)  $47 \pm 1.753 \frac { 5 } { \sqrt { 15 } }$ 
B)  $47 \pm 1.761 \frac { 5 } { \sqrt { 15 } }$ 
C)  $47 \pm 1.645 \frac { 5 } { \sqrt { 15 } }$ 
D)  $47 \pm 1.345 \frac { 5 } { \sqrt { 15 } }$

Question 10

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood.

$X =$ sale_price

SAMPLE MEAN OF X $= 46,300$
SAMPLE STANDARD DEV $= 13,747$
'SAMPLE SIZE OF $X = \quad 15$
CONFIDENCE $= \quad 95$

UPPER LIMIT $= \quad 53,913.6$
SAMPLE MEAN OF $X = \quad 46,300$
LOWER LIMIT $= \quad 38,686.4$

At what level of reliability is the confidence interval made?

Accepted Answer

A)  52.5% 
B)  95% 
C)  5% 
D)  47.5% 
A)  52.5% 
B)  95% 
C)  5% 
D)  47.5%

Question 11

Which statement best describes a parameter?

Accepted Answer

A)  A parameter is an unbiased estimate of a statistic found by experimentation or polling. 
B)  A parameter is a numerical measure of a population that is almost always unknown and must be estimated. 
C)  A parameter is a sample size that guarantees the error in estimation is within acceptable limits. 
D)  A parameter is a level of confidence associated with an interval about a sample mean or proportion. 
A)  A parameter is an unbiased estimate of a statistic found by experimentation or polling. 
B)  A parameter is a numerical measure of a population that is almost always unknown and must be estimated. 
C)  A parameter is a sample size that guarantees the error in estimation is within acceptable limits. 
D)  A parameter is a level of confidence associated with an interval about a sample mean or proportion.

Question 12

A random sample of $n = 144$ measurements was selected from a population with unknown mean $\mu$ and standard deviation $\sigma$. Calculate a $90 \%$ confidence interval if $\bar { x } = 3.55$ and $s =$.49

Accepted Answer

The answer of A random sample of $n = 144$...

Question 13

A random sample of 250 students at a university finds that these students take a mean of 15.3 credit hours per quarter with a standard deviation of 1.6 credit hours. Estimate the mean credit hours taken by a student each quarter using a 95% confidence interval. Round to the nearest thousandth.

Accepted Answer

A)  $15.3 \pm .198$ 
B)  $15.3 \pm .010$ 
C)  $15.3 \pm .013$ 
D)  $15.3 \pm .157$ 
A)  $15.3 \pm .198$ 
B)  $15.3 \pm .010$ 
C)  $15.3 \pm .013$ 
D)  $15.3 \pm .157$

Question 14

It is desired to estimate the average time it takes Statistics students to finish a computer project to within two hours at 90% reliability. It is estimated that the standard deviation of the times is 14 hours. How large a sample should be taken to get the desired interval?

Accepted Answer

A)  $n = 189$ 
B)  $n = 231$ 
C)  $\mathrm { n } = 325$ 
D)  $n = 133$ 
A)  $n = 189$ 
B)  $n = 231$ 
C)  $\mathrm { n } = 325$ 
D)  $n = 133$

Question 15

Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested in estimating the average parking time of students from within the various colleges on campus.
Which of the following would represent the target parameter of interest?

Accepted Answer

A)  $\mu$ 
B)  $p$ 
A)  $\mu$ 
B)  $p$

Question 16

A random sample of 4000 U.S. citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval.

Accepted Answer

A)  $.5625 \pm .0129$ 
B)  $.5625 \pm .4048$ 
C)  $.4375 \pm .4048$ 
D)  $.4375 \pm .0129$ 
A)  $.5625 \pm .0129$ 
B)  $.5625 \pm .4048$ 
C)  $.4375 \pm .4048$ 
D)  $.4375 \pm .0129$

Question 17

Find $\mathrm { z } _ { \alpha / 2 }$ for the given value of $\alpha$.
$\alpha = 0.04$

Accepted Answer

A)  2.33 
B)  2.05 
C)  1.75 
D)  0.18 
A)  2.33 
B)  2.05 
C)  1.75 
D)  0.18

Question 18

Since the population standard deviation ? is almost always known, we use it instead of the sample  standard deviation s when finding a confidence interval.

Accepted Answer

A) True 
 B)False

Question 19

A confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following confidence interval: (.438, .642).
Using the information above, what sample size would be necessary if we wanted to estimate the true proportion to within 3% using 99% reliability?

Accepted Answer

A)  1769 
B)  1842 
C)  1916 
D)  1831 
A)  1769 
B)  1842 
C)  1916 
D)  1831

Question 20

Calculate the finite population correction factor for  $\mathrm { n } = 300 \text { and } \mathrm { N } = 1500$

Accepted Answer

A)  .4472 
B)  .8000 
C)  2.000 
D)  .8944 
A)  .4472 
B)  .8000 
C)  2.000 
D)  .8944

What is the confidence coefficient in a 95% confidence interval for $\mu$ ?

When the sample size is small, confidence intervals for a population proportion are more reliable when the population proportion p is near 0 or 1.

The Central Limit Theorem guarantees an approximately normal sampling distribution for the sample mean for large sample sizes, so no knowledge about the distribution of the population is necessary for the corresponding interval to be valid.

The registrar's office at State University would like to determine a 95% confidence interval for the mean commute time of its students. A member of the staff randomly chooses a parking lot and surveys the first 125 students who park in the chosen lot on a given day. The confidence interval is

Explain what the phrase 95% confident means when we interpret a 95% confidence interval for µ.

Let $t _ { 0 }$ be a particular value of $t$ . Find a value of $t _ { 0 }$ such that $P \left( t \leq t _ { 0 } \right.$ or $\left. t \geq t _ { 0 } \right) = .1$ where $\mathrm { df } =$ 14 .

Fifteen SmartCars were randomly selected and the highway mileage of each was noted. The analysis yielded a mean of 47 miles per gallon and a standard deviation of 5 miles per gallon. Which of the following would represent a 90% confidence interval for the average highway Mileage of all SmartCars?

Which statement best describes a parameter?

A random sample of $n = 144$ measurements was selected from a population with unknown mean $\mu$ and standard deviation $\sigma$ . Calculate a $90 \%$ confidence interval if $\bar { x } = 3.55$ and $s =$ .49

A random sample of 250 students at a university finds that these students take a mean of 15.3 credit hours per quarter with a standard deviation of 1.6 credit hours. Estimate the mean credit hours taken by a student each quarter using a 95% confidence interval. Round to the nearest thousandth.

It is desired to estimate the average time it takes Statistics students to finish a computer project to within two hours at 90% reliability. It is estimated that the standard deviation of the times is 14 hours. How large a sample should be taken to get the desired interval?

A random sample of 4000 U.S. citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval.

Find $\mathrm { z } _ { \alpha / 2 }$ for the given value of $\alpha$ . $\alpha = 0.04$

Since the population standard deviation ? is almost always known, we use it instead of the sample standard deviation s when finding a confidence interval.

Calculate the finite population correction factor for $\mathrm { n } = 300 \text { and } \mathrm { N } = 1500$

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

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Exam 6: Inferences Based on a Single Sample: Estimation With Confidence Intervals

What is the confidence coefficient in a 95% confidence interval for μ\muμ ?

When the sample size is small, confidence intervals for a population proportion are more reliable when the population proportion p is near 0 or 1.

The Central Limit Theorem guarantees an approximately normal sampling distribution for the sample mean for large sample sizes, so no knowledge about the distribution of the population is necessary for the corresponding interval to be valid.

The registrar's office at State University would like to determine a 95% confidence interval for the mean commute time of its students. A member of the staff randomly chooses a parking lot and surveys the first 125 students who park in the chosen lot on a given day. The confidence interval is

Explain what the phrase 95% confident means when we interpret a 95% confidence interval for µ.

Let t0t _ { 0 }t0​ be a particular value of ttt . Find a value of t0t _ { 0 }t0​ such that P(t≤t0P \left( t \leq t _ { 0 } \right.P(t≤t0​ or t≥t0)=.1\left. t \geq t _ { 0 } \right) = .1t≥t0​)=.1 where df=\mathrm { df } =df= 14 .

Fifteen SmartCars were randomly selected and the highway mileage of each was noted. The analysis yielded a mean of 47 miles per gallon and a standard deviation of 5 miles per gallon. Which of the following would represent a 90% confidence interval for the average highway Mileage of all SmartCars?

Which statement best describes a parameter?

A random sample of n=144n = 144n=144 measurements was selected from a population with unknown mean μ\muμ and standard deviation σ\sigmaσ . Calculate a 90%90 \%90% confidence interval if xˉ=3.55\bar { x } = 3.55xˉ=3.55 and s=s =s= .49

A random sample of 250 students at a university finds that these students take a mean of 15.3 credit hours per quarter with a standard deviation of 1.6 credit hours. Estimate the mean credit hours taken by a student each quarter using a 95% confidence interval. Round to the nearest thousandth.

It is desired to estimate the average time it takes Statistics students to finish a computer project to within two hours at 90% reliability. It is estimated that the standard deviation of the times is 14 hours. How large a sample should be taken to get the desired interval?

A random sample of 4000 U.S. citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval.

Find zα/2\mathrm { z } _ { \alpha / 2 }zα/2​ for the given value of α\alphaα . α=0.04\alpha = 0.04α=0.04

Since the population standard deviation ? is almost always known, we use it instead of the sample standard deviation s when finding a confidence interval.

Calculate the finite population correction factor for n=300 and N=1500\mathrm { n } = 300 \text { and } \mathrm { N } = 1500n=300 and N=1500

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

What is the confidence coefficient in a 95% confidence interval for $\mu$ ?

Let $t _ { 0 }$ be a particular value of $t$ . Find a value of $t _ { 0 }$ such that $P \left( t \leq t _ { 0 } \right.$ or $\left. t \geq t _ { 0 } \right) = .1$ where $\mathrm { df } =$ 14 .

A random sample of $n = 144$ measurements was selected from a population with unknown mean $\mu$ and standard deviation $\sigma$ . Calculate a $90 \%$ confidence interval if $\bar { x } = 3.55$ and $s =$ .49

Find $\mathrm { z } _ { \alpha / 2 }$ for the given value of $\alpha$ . $\alpha = 0.04$

Calculate the finite population correction factor for $\mathrm { n } = 300 \text { and } \mathrm { N } = 1500$