Question 1

Express the confidence interval using the indicated format.
-Express the confidence interval  0.62<p<0.720.62 < p < 0.720.62<p<0.72  in the form of  p^±E\hat { p } \pm Ep^​±E .

Accepted Answer

A)    0.67±0.050.67 \pm 0.050.67±0.05 
B)    0.62±0.10.62 \pm 0.10.62±0.1 
C)    0.62±0.050.62 \pm 0.050.62±0.05 
D)    0.67±0.10.67 \pm 0.10.67±0.1

Question 2

Hannah selected a simple random sample of all adults in her town and, based on this sample, constructed a confidence interval for the mean salary of all adults in the town.
However, the distribution of salaries in the town is not exactly normal. Will the confidence interval still give a good estimate of the mean salary?

Accepted Answer

Yes, confidence interval procedures are ...

Question 3

The following confidence interval is obtained for a population proportion,  p:(0.734,0.778) p : ( 0.734,0.778 ) p:(0.734,0.778)   Use these confidence interval limits to find the margin of error, E.

Accepted Answer

A)   0.020
B)   0.044
C)   0.022
D)   0.023

Question 4

Describe the process for finding the confidence interval for a population proportion.

Accepted Answer

1) Find the summary statistics $\hat { \mathrm { p } }$ and $\hat { \mathrm { q } }$
2) Compute E using the z distribution and the formula
$E = { } _ { z } \alpha / 2 \cdot \sqrt { \frac { \hat { p q } } { \mathrm { n } } } .$
3) Find the interval by adding $E$ to $\hat { p }$ and then subtracting $E$ from $\hat { p }$.
4) Interpret the interval.

Question 5

Do one of the following, as appropriate: (a)  Find the critical value z?/2, (b)  find the critical value t?/2, (c)  state that neither the normal nor the t distribution applies.
- 91%;n=45;σ91 \% ; \mathrm { n } = 45 ; \sigma91%;n=45;σ  is known; population appears to be very skewed.

Accepted Answer

A)    zα/2=1.75\mathrm { z } _ { \alpha / 2 } = 1.75zα/2​=1.75 
B)    tα/2=1.34\mathrm { t } _ { \alpha / 2 } = 1.34tα/2​=1.34 
C)    zα/2=1.70\mathrm { z } _ { \alpha / 2 } = 1.70zα/2​=1.70 
D)    tα/2=1.645t _ { \alpha / 2 } = 1.645tα/2​=1.645

Question 6

Express the confidence interval using the indicated format.
-Express the confidence interval  (0.326,0.458) ( 0.326,0.458 ) (0.326,0.458)   in the form of  p^±E\hat { p } \pm \mathrm { E }p^​±E .

Accepted Answer

A)    0.392±0.0660.392 \pm 0.0660.392±0.066 
B)    0.326±0.1320.326 \pm 0.1320.326±0.132 
C)    0.392±0.1320.392 \pm 0.1320.392±0.132 
D)    0.326±0.0660.326 \pm 0.0660.326±0.066

Question 7

A one-sided confidence interval for p\mathrm { p }p can be written as pp>p^−E\mathrm { p } > \hat { \mathrm { p } } - \mathrm { E }p>p^−E where the margin of error E\mathrm { E }E is modified by replacing zα/2\mathrm { z } \alpha / 2zα/2 with zα\mathrm { z } _ { \alpha }zα . If a teacher wants to report that the fail rate on a test is at most xxx with 90%90 \%90% confidence, construct the appropriate one-sided confidence interval. Assume that a simple random sample of 52 students results in 7 who fail the test.

Accepted Answer

A) p<0.074p < 0.074p<0.074 B) p<0.212\mathrm { p } < 0.212p<0.212 C) p <0.195< 0.195<0.195 D) 0.074">p>0.074p > 0.074p>0.074

Question 8

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places.
-98% confidence; the sample size is 810, of which 20% are successes

Accepted Answer

A)   0.0275
B)   0.0288
C)   0.0327
D)   0.0362

Question 9

Why would manufacturers and businesses be interested in constructing a confidence interval for the population variance? Would manufacturers and businesses want large or small variances?

Accepted Answer

Manufacturers and businesses would be in...

Question 10

Express the confidence interval using the indicated format.
-Express the confidence interval  −0.061<p<0.579- 0.061 < \mathrm { p } < 0.579−0.061<p<0.579  in the form of  p^±E\hat { \mathrm { p } } \pm \mathrm { E }p^​±E .

Accepted Answer

A)    0.259±0.320.259 \pm 0.320.259±0.32 
B)    0.259−0.320.259 - 0.320.259−0.32 
C)    0.259±0.50.259 \pm 0.50.259±0.5 
D)    0.32±0.50.32 \pm 0.50.32±0.5 A

Question 11

To be able to say with 95% confidence level that the standard deviation of a data set is within 10% of the population's standard deviation, the number of observations within the data set must be greater than or equal to what quantity?

Accepted Answer

A)   805
B)   335
C)   250
D)   192

Question 12

Use the confidence level and sample data to find a confidence interval for estimating the population µ. Round your answer to the same number of decimal places as the sample mean.
-A laboratory tested 73 chicken eggs and found that the mean amount of cholesterol was 230 milligrams with  σ=17.4\sigma = 17.4σ=17.4  milligrams. Construct a  95%95 \%95%  confidence interval for the true mean cholesterol content,  μ\muμ , of all such eggs.

Accepted Answer

A)    225mg<μ<234mg225 \mathrm { mg } < \mu < 234 \mathrm { mg }225mg<μ<234mg 
B)    225mg<μ<233mg225 \mathrm { mg } < \mu < 233 \mathrm { mg }225mg<μ<233mg 
C)    226mg<μ<234mg226 \mathrm { mg } < \mu < 234 \mathrm { mg }226mg<μ<234mg 
D)    227mg<μ<235mg227 \mathrm { mg } < \mu < 235 \mathrm { mg }227mg<μ<235mg

Question 13

Use the given data to find the minimum sample size required to estimate the population proportion.
-Margin of error: 0.044; confidence level: 95%;  p^\hat{p}p^​  and  q^\hat{q}q^​  unknown

Accepted Answer

A)   635
B)   497
C)   352
D)   405

Question 14

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ.
Assume that the population has a normal distribution. Round the confidence interval limits to the same number of
decimal places as the sample standard deviation.
-To find the standard deviation of the diameter of wooden dowels, the manufacturer measures 19 randomly selected dowels and finds the standard deviation of the sample to be  s=0.16s = 0.16s=0.16 . Find the 95\% confidence interval for the population standard deviation  σ\sigmaσ .

Accepted Answer

A)    0.13<σ<0.220.13 < \sigma < 0.220.13<σ<0.22 
B)    0.11<σ<0.250.11 < \sigma < 0.250.11<σ<0.25 
C)    0.15<σ<0.210.15 < \sigma < 0.210.15<σ<0.21 
D)    0.12<σ<0.240.12 < \sigma < 0.240.12<σ<0.24

Question 15

Find the critical value  xL2x _ { L } ^ { 2 }xL2​  corresponding to a sample size of 4 and a confidence level of 95 percent.

Accepted Answer

A)   7.815
B)   9.348
C)   0.216
D)   0.352

Question 16

Under what three conditions is it appropriate to use the t distribution in place of the standard normal distribution?

Accepted Answer

1) $\mathrm { n } \leq 30$
2) $\sigma$ is unknown, and
3) the parent population is essentially normal

Question 17

A paper published the results of a poll. It stated that, based on a sample of 1000 married men, 51% of married men say that they would marry the same woman again. The margin of error was given as ±3 percentage points and the confidence level was given as 95%.
What does it mean that the margin of error was ±3 percentage points?

Accepted Answer

If 51% is used as an estimate of the per...

Question 18

Draw a diagram of the chi-square distribution. Discuss its shape and values.

Accepted Answer

The following graph illustrates examples...

Question 19

n=51,x=23;95%\mathrm { n } = 51 , \mathrm { x } = 23 ; 95 \%n=51,x=23;95%  confidence

Accepted Answer

A)    0.336<p<0.5660.336 < p < 0.5660.336<p<0.566 
B)    0.313<p<0.5890.313 < p < 0.5890.313<p<0.589 
C)    0.335<p<0.5670.335 < p < 0.5670.335<p<0.567 
D)    0.314<p<0.5880.314 < p < 0.5880.314<p<0.588

Question 20

Find the critical value  χR2\chi { } _ { \mathrm { R } } ^ { 2 }χR2​  corresponding to a sample size of 19 and a confidence level of 99 percent.

Accepted Answer

A)    34.80534.80534.805 
B)    37.15637.15637.156 
C)    6.2656.2656.265 
D)    7.0157.0157.015

Exam 7: Estimates and Sample Size

Express the confidence interval using the indicated format. -Express the confidence interval $0.62 < p < 0.72$ in the form of $\hat { p } \pm E$ .

Correct Answer
verified

Correct Answer
verified
Yes, confidence interval procedures are ...
View Answer

The following confidence interval is obtained for a population proportion, $p : ( 0.734,0.778 )$ Use these confidence interval limits to find the margin of error, E.

Correct Answer
verified

Describe the process for finding the confidence interval for a population proportion.

Do one of the following, as appropriate: (a) Find the critical value z?/2, (b) find the critical value t?/2, (c) state that neither the normal nor the t distribution applies. - $91 \% ; \mathrm { n } = 45 ; \sigma$ is known; population appears to be very skewed.

Correct Answer
verified

Express the confidence interval using the indicated format. -Express the confidence interval $( 0.326,0.458 )$ in the form of $\hat { p } \pm \mathrm { E }$ .

Correct Answer
verified

Correct Answer
verified

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. -98% confidence; the sample size is 810, of which 20% are successes

Correct Answer
verified

Why would manufacturers and businesses be interested in constructing a confidence interval for the population variance? Would manufacturers and businesses want large or small variances?

Correct Answer
verified
Manufacturers and businesses would be in...
View Answer

Express the confidence interval using the indicated format. -Express the confidence interval $- 0.061 < \mathrm { p } < 0.579$ in the form of $\hat { \mathrm { p } } \pm \mathrm { E }$ .

Correct Answer
verified
A

To be able to say with 95% confidence level that the standard deviation of a data set is within 10% of the population's standard deviation, the number of observations within the data set must be greater than or equal to what quantity?

Correct Answer
verified

Correct Answer
verified

Use the given data to find the minimum sample size required to estimate the population proportion. -Margin of error: 0.044; confidence level: 95%; $\hat{p}$ and $\hat{q}$ unknown

Correct Answer
verified

Correct Answer
verified

Find the critical value $x _ { L } ^ { 2 }$ corresponding to a sample size of 4 and a confidence level of 95 percent.

Correct Answer
verified

Under what three conditions is it appropriate to use the t distribution in place of the standard normal distribution?

Correct Answer
verified
1) \(\mathrm { n } \leq 30\) 2) \(\sigma\) is unknown, and 3) the parent population is essentially normal

Correct Answer
verified
If 51% is used as an estimate of the per...
View Answer

Draw a diagram of the chi-square distribution. Discuss its shape and values.

Correct Answer
verified
The following graph illustrates examples...
View Answer

$\mathrm { n } = 51 , \mathrm { x } = 23 ; 95 \%$ confidence

Correct Answer
verified

Find the critical value $\chi { } _ { \mathrm { R } } ^ { 2 }$ corresponding to a sample size of 19 and a confidence level of 99 percent.

Correct Answer
verified

Exam 7: Estimates and Sample Size

Express the confidence interval using the indicated format. -Express the confidence interval 0.62<p<0.720.62 < p < 0.720.62<p<0.72 in the form of p^±E\hat { p } \pm Ep^​±E .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedYes, confidence interval procedures are ...View AnswerShow Answer

The following confidence interval is obtained for a population proportion, p:(0.734,0.778) p : ( 0.734,0.778 ) p:(0.734,0.778) Use these confidence interval limits to find the margin of error, E.

Correct AnswerverifiedShow Answer

Describe the process for finding the confidence interval for a population proportion.

Do one of the following, as appropriate: (a) Find the critical value z?/2, (b) find the critical value t?/2, (c) state that neither the normal nor the t distribution applies. - 91%;n=45;σ91 \% ; \mathrm { n } = 45 ; \sigma91%;n=45;σ is known; population appears to be very skewed.

Correct AnswerverifiedShow Answer

Express the confidence interval using the indicated format. -Express the confidence interval (0.326,0.458) ( 0.326,0.458 ) (0.326,0.458) in the form of p^±E\hat { p } \pm \mathrm { E }p^​±E .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. -98% confidence; the sample size is 810, of which 20% are successes

Correct AnswerverifiedShow Answer

Why would manufacturers and businesses be interested in constructing a confidence interval for the population variance? Would manufacturers and businesses want large or small variances?

Correct AnswerverifiedManufacturers and businesses would be in...View AnswerShow Answer

Express the confidence interval using the indicated format. -Express the confidence interval −0.061<p<0.579- 0.061 < \mathrm { p } < 0.579−0.061<p<0.579 in the form of p^±E\hat { \mathrm { p } } \pm \mathrm { E }p^​±E .

Correct AnswerverifiedA

To be able to say with 95% confidence level that the standard deviation of a data set is within 10% of the population's standard deviation, the number of observations within the data set must be greater than or equal to what quantity?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Use the given data to find the minimum sample size required to estimate the population proportion. -Margin of error: 0.044; confidence level: 95%; p^\hat{p}p^​ and q^\hat{q}q^​ unknown

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find the critical value xL2x _ { L } ^ { 2 }xL2​ corresponding to a sample size of 4 and a confidence level of 95 percent.

Correct AnswerverifiedShow Answer

Under what three conditions is it appropriate to use the t distribution in place of the standard normal distribution?

Correct Answerverified1) \(\mathrm { n } \leq 30\) 2) \(\sigma\) is unknown, and 3) the parent population is essentially normal

Correct AnswerverifiedIf 51% is used as an estimate of the per...View AnswerShow Answer

Draw a diagram of the chi-square distribution. Discuss its shape and values.

Correct AnswerverifiedThe following graph illustrates examples...View AnswerShow Answer

n=51,x=23;95%\mathrm { n } = 51 , \mathrm { x } = 23 ; 95 \%n=51,x=23;95% confidence

Correct AnswerverifiedShow Answer

Find the critical value χR2\chi { } _ { \mathrm { R } } ^ { 2 }χR2​ corresponding to a sample size of 19 and a confidence level of 99 percent.

Correct AnswerverifiedShow Answer

Express the confidence interval using the indicated format. -Express the confidence interval $0.62 < p < 0.72$ in the form of $\hat { p } \pm E$ .

Correct Answer
verified

Correct Answer
verified
Yes, confidence interval procedures are ...
View Answer

The following confidence interval is obtained for a population proportion, $p : ( 0.734,0.778 )$ Use these confidence interval limits to find the margin of error, E.

Correct Answer
verified

Do one of the following, as appropriate: (a) Find the critical value z?/2, (b) find the critical value t?/2, (c) state that neither the normal nor the t distribution applies. - $91 \% ; \mathrm { n } = 45 ; \sigma$ is known; population appears to be very skewed.

Correct Answer
verified

Express the confidence interval using the indicated format. -Express the confidence interval $( 0.326,0.458 )$ in the form of $\hat { p } \pm \mathrm { E }$ .

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified
Manufacturers and businesses would be in...
View Answer

Express the confidence interval using the indicated format. -Express the confidence interval $- 0.061 < \mathrm { p } < 0.579$ in the form of $\hat { \mathrm { p } } \pm \mathrm { E }$ .

Correct Answer
verified
A

Correct Answer
verified

Correct Answer
verified

Use the given data to find the minimum sample size required to estimate the population proportion. -Margin of error: 0.044; confidence level: 95%; $\hat{p}$ and $\hat{q}$ unknown

Correct Answer
verified

Correct Answer
verified

Find the critical value $x _ { L } ^ { 2 }$ corresponding to a sample size of 4 and a confidence level of 95 percent.

Correct Answer
verified

Correct Answer
verified
1) \(\mathrm { n } \leq 30\) 2) \(\sigma\) is unknown, and 3) the parent population is essentially normal

Correct Answer
verified
If 51% is used as an estimate of the per...
View Answer

Correct Answer
verified
The following graph illustrates examples...
View Answer

$\mathrm { n } = 51 , \mathrm { x } = 23 ; 95 \%$ confidence

Correct Answer
verified

Find the critical value $\chi { } _ { \mathrm { R } } ^ { 2 }$ corresponding to a sample size of 19 and a confidence level of 99 percent.

Correct Answer
verified