Question 1

Construct a $99 \%$ confidence interval for $n=42, \bar{x}=18.2$, and $\sigma=3.96$.

Accepted Answer

A)  $16.63<\mu<19.77$ 
B)  $17.00<\mu<19.40$ 
C)  $17.00<\mu<19.77$ 
D)  $16.63<\mu<19.40$ 
A)  $16.63<\mu<19.77$ 
B)  $17.00<\mu<19.40$ 
C)  $17.00<\mu<19.77$ 
D)  $16.63<\mu<19.40$ A

Question 2

The exact shape of the $t$ distribution depends on a parameter called the __________

Accepted Answer

A)  degrees of freedom 
B)  confidence level 
C)  Student's $t$ distribution 
D)  $t$ statistic 
A)  degrees of freedom 
B)  confidence level 
C)  Student's $t$ distribution 
D)  $t$ statistic A

Question 3

The formula for the maximum error of estimation is

Accepted Answer

A)  $E=z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{2 n}}$. 
B)  $E=z_{\alpha} \cdot \frac{\sigma}{\sqrt{n}}$. 
C)  $E=z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}$. 
D)  $E=z_{\alpha / 2} \cdot \frac{\sigma}{n}$. 
A)  $E=z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{2 n}}$. 
B)  $E=z_{\alpha} \cdot \frac{\sigma}{\sqrt{n}}$. 
C)  $E=z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}$. 
D)  $E=z_{\alpha / 2} \cdot \frac{\sigma}{n}$. C

Question 4

Susan wants fo find a $99 \%$ confidence interval for the time it takes her to drive home from school. She kept records for 15 days and found her average time to drive was 17.5 minutes with a standard deviation of 4.7 minutes. Calculate Susan's maximum error of estimate.

Accepted Answer

A)  2.38 
B)  3.12 
C)  2.11 
D)  1.68 
A)  2.38 
B)  3.12 
C)  2.11 
D)  1.68

Question 5

$\bar{x}-z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}<\mu<\bar{x}+z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}$ is an example of $\mathrm{a}(\mathrm{n})$

Accepted Answer

A)  confidence interval. 
B)  interval estimate. 
C)  distribution interval. 
D)  confidence limit. 
A)  confidence interval. 
B)  interval estimate. 
C)  distribution interval. 
D)  confidence limit.

Question 6

Suppose that a highway patrol person wants to estimate what proportion of all drivers drive over the speed limit, and she wants to be able to assert with probability of at least 0.95 that its error will not exceed 0.07 . How large a sample will be needed if she knows that the true proportion lies somewhere on the interval from 0.6 or 0.7 ?

Accepted Answer

A)  $n=165$ 
B)  $n=196$ 
C)  $n=189$ 
D)  $n=188.2$ 
A)  $n=165$ 
B)  $n=196$ 
C)  $n=189$ 
D)  $n=188.2$

Question 7

When constructing confidence intervals for $\sigma$ based on $s$, it requires that the population we are sampling has roughly the shape of __________.

Accepted Answer

A)  a normal distribution 
B)  a straight line 
C)  a uniform distribution 
D)  a chi-square distribution 
A)  a normal distribution 
B)  a straight line 
C)  a uniform distribution 
D)  a chi-square distribution

Question 8

A survey randomly selected 250 top executives. The average height of these executives was 66.9 inches with a standard deviation of 6.2 inches. What is a 95\% confidence interval for the mean height, $\mu$, of all top executives?

Accepted Answer

A)  $66.1<\mu<67.7$ 
B)  $65.3<\mu<68.5$ 
C)  $62.8<\mu<66.8$ 
D)  $63.5<\mu<66.1$ 
A)  $66.1<\mu<67.7$ 
B)  $65.3<\mu<68.5$ 
C)  $62.8<\mu<66.8$ 
D)  $63.5<\mu<66.1$

Question 9

A quality control engineer intends to use the mean of a random sample of $n=85$ to estimate the average time it takes to manufacture an item. If, based on experience, the engineer can assume that $\sigma=4.8$ hours for such data, what can he assert with probability 0.99 about the maximum error of the estimate?

Accepted Answer

A)  $E \approx 1.34$ hours 
B)  $E \approx 0.13$ hours 
C)  $E \approx 0.15$ hours 
D)  $E \approx 1.21$ hours 
A)  $E \approx 1.34$ hours 
B)  $E \approx 0.13$ hours 
C)  $E \approx 0.15$ hours 
D)  $E \approx 1.21$ hours

Question 10

If $n=325$ and $\sigma=8.3$, what is the maximum error of estimate with a probability of 0.95 ?

Accepted Answer

A)  0.05 
B)  1.19 
C)  0.90 
D)  0.75 
A)  0.05 
B)  1.19 
C)  0.90 
D)  0.75

Question 11

In general, we make __________ about future values of random variables and __________ once the data have been obtained.

Accepted Answer

A)  confidence statements; probability statements 
B)  estimation statements; confidence statements 
C)  probability statements; confidence statements 
D)  probability statements; estimation statements 
A)  confidence statements; probability statements 
B)  estimation statements; confidence statements 
C)  probability statements; confidence statements 
D)  probability statements; estimation statements

Question 12

A professor wants to use the mean of a random sample to estimate the average amount of time students take to do their homework. He wants to be able to assert with a probability of 0.99 that his error will be at most 15 minutes. If $\sigma=29$ minutes, how large a sample will he need?

Accepted Answer

A)  15 
B)  14 
C)  25 
D)  4 
A)  15 
B)  14 
C)  25 
D)  4

Question 13

Suppose that $\bar{x}=81$ is being used as an estimate of the true average score for students' first exam in psychology. What can be said with $95 \%$ confidence about the maximum error if $n=11$ and $s=5$ ?

Accepted Answer

A)  $E \approx 2.73$ 
B)  $E \approx 3.32$ 
C)  $E \approx 3.36$ 
D)  $E \approx 2.71$ 
A)  $E \approx 2.73$ 
B)  $E \approx 3.32$ 
C)  $E \approx 3.36$ 
D)  $E \approx 2.71$

Construct a $99 \%$ confidence interval for $n=42, \bar{x}=18.2$ , and $\sigma=3.96$ .

The exact shape of the $t$ distribution depends on a parameter called the __________

The formula for the maximum error of estimation is

Susan wants fo find a $99 \%$ confidence interval for the time it takes her to drive home from school. She kept records for 15 days and found her average time to drive was 17.5 minutes with a standard deviation of 4.7 minutes. Calculate Susan's maximum error of estimate.

$\bar{x}-z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}<\mu<\bar{x}+z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}$ is an example of $\mathrm{a}(\mathrm{n})$

When constructing confidence intervals for $\sigma$ based on $s$ , it requires that the population we are sampling has roughly the shape of __________.

A survey randomly selected 250 top executives. The average height of these executives was 66.9 inches with a standard deviation of 6.2 inches. What is a 95\% confidence interval for the mean height, $\mu$ , of all top executives?

If $n=325$ and $\sigma=8.3$ , what is the maximum error of estimate with a probability of 0.95 ?

In general, we make about future values of random variables and once the data have been obtained.

A professor wants to use the mean of a random sample to estimate the average amount of time students take to do their homework. He wants to be able to assert with a probability of 0.99 that his error will be at most 15 minutes. If $\sigma=29$ minutes, how large a sample will he need?

Suppose that $\bar{x}=81$ is being used as an estimate of the true average score for students' first exam in psychology. What can be said with $95 \%$ confidence about the maximum error if $n=11$ and $s=5$ ?

Introduction

Summarizing Data: Listing and Grouping

Summarizing Data: Measures of Location

Summarizing Data: Measures of Variation

Possibilities and Probabilities

Some Rules of Probability

Expectations and Decisions

Probability Distributions

The Normal Distribution

Sampling and Sampling Distributions

Tests of Hypotheses: Means

Tests of Hypotheses: Standard Deviations

Tests of Hypotheses Based on Count Data

Analysis of Variance

Regression

Correlation

Nonparametric Tests

Filters

Exam 11: Problems of Estimation

Construct a 99%99 \%99% confidence interval for n=42,xˉ=18.2n=42, \bar{x}=18.2n=42,xˉ=18.2 , and σ=3.96\sigma=3.96σ=3.96 .

The exact shape of the ttt distribution depends on a parameter called the __________

The formula for the maximum error of estimation is

Susan wants fo find a 99%99 \%99% confidence interval for the time it takes her to drive home from school. She kept records for 15 days and found her average time to drive was 17.5 minutes with a standard deviation of 4.7 minutes. Calculate Susan's maximum error of estimate.

xˉ−zα/2⋅σn<μ<xˉ+zα/2⋅σn\bar{x}-z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}<\mu<\bar{x}+z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}xˉ−zα/2​⋅n​σ​<μ<xˉ+zα/2​⋅n​σ​ is an example of a(n)\mathrm{a}(\mathrm{n})a(n)

When constructing confidence intervals for σ\sigmaσ based on sss , it requires that the population we are sampling has roughly the shape of __________.

A survey randomly selected 250 top executives. The average height of these executives was 66.9 inches with a standard deviation of 6.2 inches. What is a 95\% confidence interval for the mean height, μ\muμ , of all top executives?

If n=325n=325n=325 and σ=8.3\sigma=8.3σ=8.3 , what is the maximum error of estimate with a probability of 0.95 ?

In general, we make __________ about future values of random variables and __________ once the data have been obtained.

A professor wants to use the mean of a random sample to estimate the average amount of time students take to do their homework. He wants to be able to assert with a probability of 0.99 that his error will be at most 15 minutes. If σ=29\sigma=29σ=29 minutes, how large a sample will he need?

Suppose that xˉ=81\bar{x}=81xˉ=81 is being used as an estimate of the true average score for students' first exam in psychology. What can be said with 95%95 \%95% confidence about the maximum error if n=11n=11n=11 and s=5s=5s=5 ?

Introduction

Summarizing Data: Listing and Grouping

Summarizing Data: Measures of Location

Summarizing Data: Measures of Variation

Possibilities and Probabilities

Some Rules of Probability

Expectations and Decisions

Probability Distributions

The Normal Distribution

Sampling and Sampling Distributions

Tests of Hypotheses: Means

Tests of Hypotheses: Standard Deviations

Tests of Hypotheses Based on Count Data

Analysis of Variance

Regression

Correlation

Nonparametric Tests

Filters

Construct a $99 \%$ confidence interval for $n=42, \bar{x}=18.2$ , and $\sigma=3.96$ .

The exact shape of the $t$ distribution depends on a parameter called the __________

Susan wants fo find a $99 \%$ confidence interval for the time it takes her to drive home from school. She kept records for 15 days and found her average time to drive was 17.5 minutes with a standard deviation of 4.7 minutes. Calculate Susan's maximum error of estimate.

$\bar{x}-z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}<\mu<\bar{x}+z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}$ is an example of $\mathrm{a}(\mathrm{n})$

When constructing confidence intervals for $\sigma$ based on $s$ , it requires that the population we are sampling has roughly the shape of __________.

A survey randomly selected 250 top executives. The average height of these executives was 66.9 inches with a standard deviation of 6.2 inches. What is a 95\% confidence interval for the mean height, $\mu$ , of all top executives?

If $n=325$ and $\sigma=8.3$ , what is the maximum error of estimate with a probability of 0.95 ?

In general, we make about future values of random variables and once the data have been obtained.

A professor wants to use the mean of a random sample to estimate the average amount of time students take to do their homework. He wants to be able to assert with a probability of 0.99 that his error will be at most 15 minutes. If $\sigma=29$ minutes, how large a sample will he need?

Suppose that $\bar{x}=81$ is being used as an estimate of the true average score for students' first exam in psychology. What can be said with $95 \%$ confidence about the maximum error if $n=11$ and $s=5$ ?