Question 1

State the Properties of Student s t-Distribution
-Which of the following is not a characteristic of Students t distribution

Accepted Answer

A)  mean of 1 
B)  symmetric distribution 
C)  depends on degrees of freedom. 
D)  For large samples, the t and z distributions are nearly equivalent. 
A)  mean of 1 
B)  symmetric distribution 
C)  depends on degrees of freedom. 
D)  For large samples, the t and z distributions are nearly equivalent. A

Question 2

Construct and Interpret a Confidence Interval for a Pop Mean, Assuming that the Pop Std Dev is Known
-Compute the critical value $\mathrm { z } \alpha / 2$ that corresponds to a $99 \%$ level of confidence.

Accepted Answer

A)  $2.575$ 
B)  $1.96$ 
C)  $1.645$ 
D)  $2.33$ 
A)  $2.575$ 
B)  $1.96$ 
C)  $1.645$ 
D)  $2.33$ A

Question 3

Explain the Role of Margin of Error in Constructing a Confidence Interval
-A certain confidence in interval is 8.15 < < 9.45. Find the sample mean x and the margin of error E.

Accepted Answer

$$\text { Sample mean } \bar { x } = 8.80 \text { and the mars }$$ gin of error, E = 0.65.

Question 4

Choose the one alternative that best completes the statement or answers the question.
-The cell phone conversations of a random sample of 50 students has a standard deviation of 9.7 minutes. Find the margin of error, E, using a 90% confidence interval.

Accepted Answer

A)  2.26 
B)  0.32 
C)  1.37 
D)  1.23 
A)  2.26 
B)  0.32 
C)  1.37 
D)  1.23

Question 5

Provide an appropriate response.
-True or False: The general form of a large-sample $( 1 - \alpha ) 100 \%$ confidence interval for a population proportion interest.

Accepted Answer

A)  True 
B)  False 
A)  True 
B)  False

Question 6

Provide an appropriate response.
-The July utility bills (in dollars) of 20 randomly selected homeowners in one city are listed below. Construct a $99 \%$ confidence interval for the variance, $\sigma ^ { 2 }$. Assume the population is normally distributed.
$\begin{array} { l l l l l l l l l l } 70 & 72 & 71 & 70 & 69 & 73 & 69 & 68 & 70 & 71 \end{array}$
$\begin{array} { l l l l l l l l l l } 67 & 71 & 70 & 74 & 69 & 68 & 71 & 71 & 71 & 72 \end{array}$

Accepted Answer

The answer of Provide an appropriate response.
-The July utility bills...

Question 7

Provide an appropriate response.
-True or False? When choosing the sample size for estimating a population proportion $\mathrm { p }$ to within $\mathrm { E }$ units with confidence $( 1 - \alpha ) 100 \%$, if you take $\mathrm { p } \approx 0.5$ as the approximation to p, you will always obtain a sample size that is at least as large as required.

Accepted Answer

A)  True 
B)  False 
A)  True 
B)  False

Question 8

Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error
-In order to set rates, an insurance company is trying to estimate the number of sick days that full time workers at a local bank take per year. A previous study indicated that the standard deviation was 2.5 days. a) How large a sample must be selected if the company wants to be 98% confident that the true mean differs from the sample mean by no more than 1 day b) Repeat part (a) using a 99% confidence interval. Which level of confidence requires a larger sample size Explain.

Accepted Answer

a) 34
b) 42 ; A @#LAT-DLM& confidence in

Question 9

Find Critical Values for the Chi-Square Distribution
-True or False: The chi-square distribution is a symmetric distribution is negative when the degrees of freedom become large.

Accepted Answer

A)  False 
B)  True 
A)  False 
B)  True

Question 10

Provide an appropriate response.
-A private opinion poll is conducted for a politician to determine what proportion of the population favors adding more national parks. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 5%

Accepted Answer

A)  664 
B)  543 
C)  1327 
D)  13 
A)  664 
B)  543 
C)  1327 
D)  13

Question 11

Provide an appropriate response.
-An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that $46 \%$ would like more discussion about the family's financial situation, $37 \%$ would like to talk about school, and $30 \%$ would like to talk about religion. These and other percentages were based on a national sampling of 502 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a $95 \%$ confidence level.

Accepted Answer

A)  $0.37 \pm 0.042$ 
B)  $0.37 \pm 0.002$ 
C)  $0.63 \pm 0.042$ 
D)  $0.63 \pm 0.002$ 
A)  $0.37 \pm 0.042$ 
B)  $0.37 \pm 0.002$ 
C)  $0.63 \pm 0.042$ 
D)  $0.63 \pm 0.002$

Question 12

Provide an appropriate response.
-A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within $3 \%$ with $90 \%$ reliability, how many students would need to be sampled?

Accepted Answer

A)  728 
B)  176 
C)  443 
D)  22 
A)  728 
B)  176 
C)  443 
D)  22

Question 13

Provide an appropriate response.
-A confidence interval for $p$ can be constructed using

Accepted Answer

A)  $\hat { \mathrm { p } } \pm \mathrm { z } _ { \alpha / 2 } \sqrt { \frac { \hat { \mathrm { p } ( 1 - \hat { \mathrm { p } ) } } } { }$ 
B)  $\mathrm { p } \pm \mathrm { z } \frac { \sigma } { \mathrm { n } }$ 
C)  $\hat { p } \pm z \sqrt { \frac { \sigma } { n } }$ 
D)  $\mathrm { p } \pm \mathrm { z } _ { \alpha / 2 } \sqrt { \frac { \mathrm { p } ( 1 - \mathrm { p } ) } { \mathrm { n } } }$ 
A)  $\hat { \mathrm { p } } \pm \mathrm { z } _ { \alpha / 2 } \sqrt { \frac { \hat { \mathrm { p } ( 1 - \hat { \mathrm { p } ) } } } { }$ 
B)  $\mathrm { p } \pm \mathrm { z } \frac { \sigma } { \mathrm { n } }$ 
C)  $\hat { p } \pm z \sqrt { \frac { \sigma } { n } }$ 
D)  $\mathrm { p } \pm \mathrm { z } _ { \alpha / 2 } \sqrt { \frac { \mathrm { p } ( 1 - \mathrm { p } ) } { \mathrm { n } } }$

Question 14

Provide an appropriate response.
-A local outdoor equipment store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100,000 items in order to determine the proportion of merchandise that is outdated. The current owners have never determined their outdated percentage and can not help the buyers. Approximately how large a sample do the buyers need in order to insure that they are $98 \%$ confident that the margin of error is within $2 \%$ ?

Accepted Answer

A)  3394 
B)  6787 
C)  13,573 
D)  1457 
A)  3394 
B)  6787 
C)  13,573 
D)  1457

Question 15

Provide an appropriate response.
-Construct a $95 \%$ confidence interval for the population mean, $\mu$. Assume the population has a normal distribution. A random sample of 16 lithium batteries has a mean life of 645 hours with a standard deviation of 31 hours.

Accepted Answer

A)  $( 628.5,661.5 )$ 
B)  $( 876.2,981.5 )$ 
C)  $( 531.2,612.9 )$ 
D)  $( 321.7,365.8 )$ 
A)  $( 628.5,661.5 )$ 
B)  $( 876.2,981.5 )$ 
C)  $( 531.2,612.9 )$ 
D)  $( 321.7,365.8 )$

Question 16

Construct a 95% Z-interval or a 95% t-interval about the population mean. Assume the data come from a population that
is approximately normal with no outliers.
-The heights of 20 - to 29 -year-old females are known to have a population standard deviation $\sigma = 2.7$ inches. A simple random sample of $n = 15$ females 20 to 29 years old results in the following data:
$\begin{array}{lllll}
63.1 & 67.9 & 64.8 & 62.2 & 65.4 \
\hline 63.3 & 66.2 & 68.2 & 69.7 & 64.1 \
\hline 68.4 & 69.9 & 67.3 & 64.5 & 70.2
\end{array}$

Accepted Answer

A)  $( 64.98,67.72 )$; we are $95 \%$ confident that the mean height of 20 - to 29 -year-old females is between $64.98$ and $67.72$ inches. 
B)  $( 64.85,67.85 )$; we are $95 \%$ confident that the mean height of 20 - to 29 -year-old females is between $64.85$ and $67.85$ inches. 
C)  $( 65.12,67.58 )$; we are $95 \%$ confident that the mean height of 20 - to 29 -year-old females is between $65.12$ and $67.58$ inches. 
D)  $( 65.20,67.50 )$; we are $95 \%$ confident that the mean height of 20 - to 29 -year-old females is between $65.20$ and $67.50$ inches. 
A)  $( 64.98,67.72 )$; we are $95 \%$ confident that the mean height of 20 - to 29 -year-old females is between $64.98$ and $67.72$ inches. 
B)  $( 64.85,67.85 )$; we are $95 \%$ confident that the mean height of 20 - to 29 -year-old females is between $64.85$ and $67.85$ inches. 
C)  $( 65.12,67.58 )$; we are $95 \%$ confident that the mean height of 20 - to 29 -year-old females is between $65.12$ and $67.58$ inches. 
D)  $( 65.20,67.50 )$; we are $95 \%$ confident that the mean height of 20 - to 29 -year-old females is between $65.20$ and $67.50$ inches.

Question 17

Provide an appropriate response.
-What effect will an outlier have on a confidence interval that is based on a small sample size?

Accepted Answer

A)  The confidence interval will be wider than an interval without the outlier. 
B)  The interval will be smaller than an interval without the outlier. 
C)  The interval will be the same with or without the outlier. 
D)  The interval will reveal exclusionary data. 
A)  The confidence interval will be wider than an interval without the outlier. 
B)  The interval will be smaller than an interval without the outlier. 
C)  The interval will be the same with or without the outlier. 
D)  The interval will reveal exclusionary data.

Question 18

Provide an appropriate response.
-True or False? When constructing a $( 1 - \alpha ) 100 \%$ confidence interval for a population variance $\sigma ^ { 2 }$, the population from which the random sample is selected can have any distribution.

Accepted Answer

A)  False 
B)  True 
A)  False 
B)  True

Question 19

Provide an appropriate response.
-Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2140 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation.

Accepted Answer

A)  $0.5350$ 
B)  2140 
C)  4000 
D)  $0.4650$ 
A)  $0.5350$ 
B)  2140 
C)  4000 
D)  $0.4650$

Question 20

Provide an appropriate response.
-A researcher wishes to estimate the number of households with two computers. How large a sample is needed in order to be $98 \%$ confident that the sample proportion will not differ from the true proportion by more than $2 \%$ ? A previous study indicates that the proportion of households with two computers is $23 \%$.

Accepted Answer

A)  2404 
B)  1701 
C)  3122 
D)  3 
A)  2404 
B)  1701 
C)  3122 
D)  3

State the Properties of Student s t-Distribution -Which of the following is not a characteristic of Students t distribution

Construct and Interpret a Confidence Interval for a Pop Mean, Assuming that the Pop Std Dev is Known -Compute the critical value $\mathrm { z } \alpha / 2$ that corresponds to a $99 \%$ level of confidence.

Explain the Role of Margin of Error in Constructing a Confidence Interval -A certain confidence in interval is 8.15 < < 9.45. Find the sample mean x and the margin of error E.

Choose the one alternative that best completes the statement or answers the question. -The cell phone conversations of a random sample of 50 students has a standard deviation of 9.7 minutes. Find the margin of error, E, using a 90% confidence interval.

Provide an appropriate response. -True or False: The general form of a large-sample $( 1 - \alpha ) 100 \%$ confidence interval for a population proportion interest.

Find Critical Values for the Chi-Square Distribution -True or False: The chi-square distribution is a symmetric distribution is negative when the degrees of freedom become large.

Provide an appropriate response. -A confidence interval for $p$ can be constructed using

Provide an appropriate response. -Construct a $95 \%$ confidence interval for the population mean, $\mu$ . Assume the population has a normal distribution. A random sample of 16 lithium batteries has a mean life of 645 hours with a standard deviation of 31 hours.

Provide an appropriate response. -What effect will an outlier have on a confidence interval that is based on a small sample size?

Provide an appropriate response. -True or False? When constructing a $( 1 - \alpha ) 100 \%$ confidence interval for a population variance $\sigma ^ { 2 }$ , the population from which the random sample is selected can have any distribution.

Data Collection

Creating Tables and Drawing Pictures of Data

Numerically Summarizing Data

Describing the Relation Between Two Variables

Probability

Discrete Probability Distributions

The Normal Probability Distribution

Sampling Distributions

Hypothesis Tests Regarding a Parameter

Inference on Two Samples

Inference on Categorical Data

Comparing Three or More Means

Inference of the Least-Squares Regression Model and Multiple Regression

Nonparametric Statistics

Filters

Exam 9: Estimating the Value of a Parameter Using Confidence Intervals