Question 1

In general, what does "degrees of freedom" refer to? Find the degrees of freedom for the
given information, assuming that you want to construct a confidence interval estimate of μ
 Six human skulls from around 4000 B.C. were measured, and the lengths have a mean of
94.2 mm and a standard deviation of 4.9 mm

Accepted Answer

The answer of In general, what does "degrees of freedom"...

Question 2

A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with $\sigma = 19,0$milligrams. Construct a  95%  confidence interval for the true mean cholesterol content,  $\mu$ of all such eggs.

Accepted Answer

A)  $223 \mathrm { mg } < \mu < 232 \mathrm { mg }$ 
B)  $224 \mathrm { mg } < \mu < 232 \mathrm { mg }$ 
C)  $225 \mathrm { mg } < \mu < 233 \mathrm { mg }$ 
D)  $223 \mathrm { mg } < \mu < 231 \mathrm { mg }$

Question 3

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

Accepted Answer

A)   37.156 
B)   6.265 
C)   34.805 
D)   7.015

Question 4

Why is $s ^ { 2 }$ the best point estimate of $\boldsymbol { \sigma } ^ { 2 }$ ?

Accepted Answer

The answer of Why is $s ^ { 2 }$...

Question 5

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

Accepted Answer

The answer of Draw a diagram of the chi-square distribution....

Question 6

Find the critical value $z _ { \alpha / 2 }$ that corresponds to a  91%  confidence level.

Accepted Answer

A)   1.34 
B)   1.645 
C)   1.70 
D)   1.75

Question 7

Find the degree of confidence used in constructing the confidence interval  0.523<p<0.669  for the population proportion  p  using sample data with  n=109, x=65 .

Accepted Answer

A)   88% 
B)   90% 
C)   95% 
D)   99%

Question 8

Under what circumstances can you replace $\sigma$ with  s  in the formula $E = z _ { a / 2 } \cdot \frac { \sigma } { \sqrt { n } } ?$

Accepted Answer

The answer of Under what circumstances can you replace $\sigma$...

Question 9

Based on a simple random sample of students from her school, Sally obtained a point
estimate of the mean weight of students at her school. What additional information would
be provided by a confidence interval estimate of the mean weight?

Accepted Answer

The answer of Based on a simple random sample of...

Question 10

You want to estimate σ for the population of waiting times at McDonald's drive-up windows,
and you want to be 95% confident that the sample standard deviation is with 20% of $$\sigma$$ Find
the minimum sample size. Is this sample size practical?

Accepted Answer

The answer of You want to estimate σ for the...

Question 11

You want to be 95% confident that the sample variance is within 40% of the population variance. Find the appropriate minimum sample size.

Accepted Answer

A) 57 
B) 224 
C) 14 
D) 11

Question 12

Fill in the blank: The critical value $z _ { \alpha / 2 }$ that corresponds to a _________% confidence level is 2.33.

Accepted Answer

A) 88 
B) 90 
C) 98 
D) 99

Question 13

Do one of the following, as appropriate: (a) Find the critical value $z _ { \alpha / 2 }$, (b) find the critical value $t _ { \alpha / 2 }$, (c) state that neither the normal nor the  t  distribution applies.
 90%  confidence interval for $\mu ; \quad n = 9 ; \sigma = 4.2$ population appears to be very skewed.

Accepted Answer

A)  $z _ { a / 2 } = 2.896$ 
B)  $z _ { \alpha / 2 } = 2.365$ 
C)  $z _ { \alpha / 2 } = 2.306$ 
D)  Neither the normal nor the  t  distribution applies.

Question 14

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion  p .
 n=56, x=30 ; 95%  confidence

Accepted Answer

A)   0.405<p<0.667 
B)   0.425<p<0.647 
C)   0.426<p<0.646 
D)   0.404<p<0.668

Question 15

Identify the distribution that applies to the following situation: In constructing a confidence interval of ? , you have 50 sample values and they appear to be
From a population with a skewed distribution. The population standard deviation is not
Known. ______________

Accepted Answer

A) Student t distribution 
B) Normal distribution 
C) Chi-square distribution 
D) None of the three distributions is appropriate.

Question 16

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 800, of which 40% are successes

Accepted Answer

A) 0.0355 
B) 0.0339 
C) 0.0404 
D) 0.0446

Question 17

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion  p .
 n=130, x=69 ; 90 %  confidence

Accepted Answer

A)   0.458<p<0.604 
B)   0.461<p<0.601 
C)   0.459<p<0.603 
D)   0.463<p<0.599

Question 18

Express a confidence interval defined as  (0.432,0.52)  in the form of the point estimate __________$\pm$ the margin of error __________
Express both in three decimal places.

Accepted Answer

A)  $0.476 \pm 0.044$ 
B)  $0.476 \pm 0.088$ 
C)  $0.432 \pm 0.088$ 
D)  $0.432 \pm 0.044$

Question 19

In a Gallup poll, 1011 adults were asked if they consume alcoholic beverages and 64% of
them said that they did. Construct a 90% confidence interval estimate of the proportion of all
adults who consume alcoholic beverages. Can we safely conclude that the majority of adults
consume alcoholic beverages?

Accepted Answer

The answer of In a Gallup poll, 1011 adults were...

Question 20

Which critical value is appropriate for a  99 %  confidence level where  n=17 ; $\sigma$ is unknown and the population appears to be normally distributed?

Accepted Answer

A)  $t _ { \alpha / 2 } = 2.898$ 
B)  $z _ { a / 2 } = 2.583$ 
C)  $t _ { \alpha / 2 } = 2.921$ 
D)  $z _ { \alpha / 2 } = 2.567$

Exam 7: Estimating Parameters and Determining Sample Sizes

A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with $\sigma = 19,0$ milligrams. Construct a 95% confidence interval for the true mean cholesterol content, $\mu$ of all such eggs.

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

Why is $s ^ { 2 }$ the best point estimate of $\boldsymbol { \sigma } ^ { 2 }$ ?

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

Find the critical value $z _ { \alpha / 2 }$ that corresponds to a 91% confidence level.

Find the degree of confidence used in constructing the confidence interval 0.523<p<0.669 for the population proportion p using sample data with n=109, x=65 .

Under what circumstances can you replace $\sigma$ with s in the formula $E = z _ { a / 2 } \cdot \frac { \sigma } { \sqrt { n } } ?$

Based on a simple random sample of students from her school, Sally obtained a point estimate of the mean weight of students at her school. What additional information would be provided by a confidence interval estimate of the mean weight?

You want to estimate σ for the population of waiting times at McDonald's drive-up windows, and you want to be 95% confident that the sample standard deviation is with 20% of $\sigma$ Find the minimum sample size. Is this sample size practical?

You want to be 95% confident that the sample variance is within 40% of the population variance. Find the appropriate minimum sample size.

Fill in the blank: The critical value $z _ { \alpha / 2 }$ that corresponds to a _________% confidence level is 2.33.

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p . n=56, x=30 ; 95% confidence

Identify the distribution that applies to the following situation: In constructing a confidence interval of ? , you have 50 sample values and they appear to be From a population with a skewed distribution. The population standard deviation is not Known. ______________

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 800, of which 40% are successes

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p . n=130, x=69 ; 90 % confidence

Express a confidence interval defined as (0.432,0.52) in the form of the point estimate $\pm$ the margin of error Express both in three decimal places.

Which critical value is appropriate for a 99 % confidence level where n=17 ; $\sigma$ is unknown and the population appears to be normally distributed?

Exam 7: Estimating Parameters and Determining Sample Sizes

A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with σ=19,0\sigma = 19,0σ=19,0 milligrams. Construct a 95% confidence interval for the true mean cholesterol content, μ\muμ of all such eggs.

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

Why is s2s ^ { 2 }s2 the best point estimate of σ2\boldsymbol { \sigma } ^ { 2 }σ2 ?

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

Find the critical value zα/2z _ { \alpha / 2 }zα/2​ that corresponds to a 91% confidence level.

Find the degree of confidence used in constructing the confidence interval 0.523<p<0.669 for the population proportion p using sample data with n=109, x=65 .

Under what circumstances can you replace σ\sigmaσ with s in the formula E=za/2⋅σn?E = z _ { a / 2 } \cdot \frac { \sigma } { \sqrt { n } } ?E=za/2​⋅n​σ​?

Based on a simple random sample of students from her school, Sally obtained a point estimate of the mean weight of students at her school. What additional information would be provided by a confidence interval estimate of the mean weight?

You want to estimate σ for the population of waiting times at McDonald's drive-up windows, and you want to be 95% confident that the sample standard deviation is with 20% of σ\sigmaσ Find the minimum sample size. Is this sample size practical?

You want to be 95% confident that the sample variance is within 40% of the population variance. Find the appropriate minimum sample size.

Fill in the blank: The critical value zα/2z _ { \alpha / 2 }zα/2​ that corresponds to a _________% confidence level is 2.33.

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p . n=56, x=30 ; 95% confidence

Identify the distribution that applies to the following situation: In constructing a confidence interval of ? , you have 50 sample values and they appear to be From a population with a skewed distribution. The population standard deviation is not Known. ______________

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 800, of which 40% are successes

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p . n=130, x=69 ; 90 % confidence

Express a confidence interval defined as (0.432,0.52) in the form of the point estimate __________ ±\pm± the margin of error __________ Express both in three decimal places.

Which critical value is appropriate for a 99 % confidence level where n=17 ; σ\sigmaσ is unknown and the population appears to be normally distributed?

A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with $\sigma = 19,0$ milligrams. Construct a 95% confidence interval for the true mean cholesterol content, $\mu$ of all such eggs.

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

Why is $s ^ { 2 }$ the best point estimate of $\boldsymbol { \sigma } ^ { 2 }$ ?

Find the critical value $z _ { \alpha / 2 }$ that corresponds to a 91% confidence level.

Under what circumstances can you replace $\sigma$ with s in the formula $E = z _ { a / 2 } \cdot \frac { \sigma } { \sqrt { n } } ?$

You want to estimate σ for the population of waiting times at McDonald's drive-up windows, and you want to be 95% confident that the sample standard deviation is with 20% of $\sigma$ Find the minimum sample size. Is this sample size practical?

Fill in the blank: The critical value $z _ { \alpha / 2 }$ that corresponds to a _________% confidence level is 2.33.

Express a confidence interval defined as (0.432,0.52) in the form of the point estimate $\pm$ the margin of error Express both in three decimal places.

Which critical value is appropriate for a 99 % confidence level where n=17 ; $\sigma$ is unknown and the population appears to be normally distributed?