Question 1

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

Question 2

In a Gallup poll of 557 randomly selected adults, 284 said that they were underpaid. Identify the best point estimate of the percentage of adults who say they are underpaid. Construct a
95% confidence interval estimate of the percentage of adults who say that that they are
underpaid. Can we safely conclude that the majority of adults say that they are underpaid?

Accepted Answer

$51.0 \% ; 46.8 \% < p < 55.1 \%$.
No, the confidence interval shows that the population percentage might be $50 \%$ or less, so we cannot safely conclude that the majority of adults say that they are underpaid.

Question 3

The following is a  95 %  confidence interval of the proportion of female medical school students: $0.449 < p < 0.511$ based on data from the American Medical Association. What is the point estimate of the proportion of females in the population of medical school students? Write a brief statement that correctly interprets the confidence interval given.

Accepted Answer

point estimate of proportion: 0.480. We have 95% confidence that the limits of 0.449 and 0.511 contain the true
value of the proportion of females in the population of medical school students.

Question 4

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

Accepted Answer

1) Find the summary

Question 5

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

Question 6

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

Question 7

Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.028; confidence level: 99%; p and q unknown

Accepted Answer

A)  1116 
B)  2223 
C)  1939 
D)  2115 
A)  1116 
B)  2223 
C)  1939 
D)  2115

Question 8

Do one of the following, as appropriate: 
(a) Find the critical value $= \alpha / 2 ,$ 
(b) find the critical value $t _ { \alpha / 2 } { } ^ { \circ }$
 99 % ; n=17 ; $\alpha$ is unknown; population appears to be normally distributed.

Accepted Answer

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

Question 9

How do you determine whether to use the z or t distribution in computing the margin of error, $E = z _ { \alpha / 2 } \cdot \frac { \sigma } { \sqrt { n } } \text { or } E = t _ { \alpha / 2 } \cdot \frac { s } { \sqrt { n } } ?$

Accepted Answer

Provided @#LAT-DLM&, the standard normal

Question 10

Identify the distribution that applies to the following situation:
In constructing a confidence interval of $\mu$, 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. 
A)  Student  t  distribution 
B)  Normal distribution 
C)  Chi-square distribution 
D)  None of the three distributions is appropriate.

Question 11

Of 380 randomly selected medical students, 21 said that they planned to work in a rural community. Find a  95 %  confidence interval for the true proportion of all medical students who plan to work in a rural community.

Accepted Answer

A)  $0.0323 < p < 0.0782$ 
B)  $0.0360 < p < 0.0745$ 
C)  $0.0251 < p < 0.0854$ 
D)  $0.0280 < p < 0.0826$ 
A)  $0.0323 < p < 0.0782$ 
B)  $0.0360 < p < 0.0745$ 
C)  $0.0251 < p < 0.0854$ 
D)  $0.0280 < p < 0.0826$

Question 12

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion  p .
 n=195, x=162 ; 95 %  confidence

Accepted Answer

A)  $0.778 < p < 0.883$ 
B)  $0.788 < p < 0.873$ 
C)  $0.789 < p < 0.873$ 
D)  $0.777 < p < 0.884$ 
A)  $0.778 < p < 0.883$ 
B)  $0.788 < p < 0.873$ 
C)  $0.789 < p < 0.873$ 
D)  $0.777 < p < 0.884$

Question 13

Use the given degree of confidence and sample data to construct a confidence interval for the population mean $\mu$ Assume that the population has a normal distribution.  n=30 , $\bar { x } = 84.6$  s=10.5,90 % confidence

Accepted Answer

A)  $79.32 < \mu < 89.88$ 
B)  $81.36 < \mu < 87.84$ 
C)  $81.34 < \mu < 87.86$ 
D)  $80.68 < \mu < 88.52$ 
A)  $79.32 < \mu < 89.88$ 
B)  $81.36 < \mu < 87.84$ 
C)  $81.34 < \mu < 87.86$ 
D)  $80.68 < \mu < 88.52$

Question 14

Define in as clear language as possible how a 95% confidence interval can be used for hypothesis tests.

Accepted Answer

In a hypothesis test at the 5%

Question 15

A group of 59 randomly selected students have a mean score of  29.5  with a standard deviation of  5.2  on a placement test. What is the  90 %  confidence interval for the mean score, $\mu$ , of all students taking the test?

Accepted Answer

A)  $28.2 < \mu < 30.8$ 
B)  $28.4 < \mu < 30.6$ 
C)  $27.8 < \mu < 31.2$ 
D)  $27.9 < \mu < 31.1$ 
A)  $28.2 < \mu < 30.8$ 
B)  $28.4 < \mu < 30.6$ 
C)  $27.8 < \mu < 31.2$ 
D)  $27.9 < \mu < 31.1$

Question 16

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 $\mu$ n=9 ; $\sigma = 4.2$ population appears to be very skewed.

Accepted Answer

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

Question 17

Express the confidence interval  (0.432,0.52)  in the form of $\hat { p } \pm \mathrm { E }$

Accepted Answer

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

Question 18

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)  $0.404 < p < 0.668$ 
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 19

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

Question 20

Fifty people are selected randomly from a certain population and it is found that 12 people in the sample are over six feet tall. What is the best point estimate of the proportion of people in the population who are over 6 feet tall?

Accepted Answer

A)  0.76 
B)  0.24 
C)  0.50 
D)  0.18 
A)  0.76 
B)  0.24 
C)  0.50 
D)  0.18

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

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

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

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

Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.028; confidence level: 99%; p and q unknown

Do one of the following, as appropriate: (a) Find the critical value $= \alpha / 2 ,$ (b) find the critical value $t _ { \alpha / 2 } { } ^ { \circ }$ 99 % ; n=17 ; $\alpha$ is unknown; population appears to be normally distributed.

How do you determine whether to use the z or t distribution in computing the margin of error, $E = z _ { \alpha / 2 } \cdot \frac { \sigma } { \sqrt { n } } \text { or } E = t _ { \alpha / 2 } \cdot \frac { s } { \sqrt { n } } ?$

Identify the distribution that applies to the following situation: In constructing a confidence interval of $\mu$ , you have 50 sample values and they appear to be from a population with a skewed distribution. The population standard deviation is not known.

Of 380 randomly selected medical students, 21 said that they planned to work in a rural community. Find a 95 % confidence interval for the true proportion of all medical students who plan to work in a rural community.

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p . n=195, x=162 ; 95 % confidence

Use the given degree of confidence and sample data to construct a confidence interval for the population mean $\mu$ Assume that the population has a normal distribution. n=30 , $\bar { x } = 84.6$ s=10.5,90 % confidence

Define in as clear language as possible how a 95% confidence interval can be used for hypothesis tests.

A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 90 % confidence interval for the mean score, $\mu$ , of all students taking the test?

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 $\mu$ n=9 ; $\sigma = 4.2$ population appears to be very skewed.

Express the confidence interval (0.432,0.52) in the form of $\hat { p } \pm \mathrm { E }$

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

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

Fifty people are selected randomly from a certain population and it is found that 12 people in the sample are over six feet tall. What is the best point estimate of the proportion of people in the population who are over 6 feet tall?

Introduction to Statistics

Exploring Data With Tables and Graphs

Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Goodness-Of-Fit and Contingency Tables

Analysis of Variance

Nonparametric Tests

Statistical Process Control

Filters

Exam 7: Estimating Parameters and Determining Sample Sizes

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

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

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

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

Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.028; confidence level: 99%; p and q unknown

Do one of the following, as appropriate: (a) Find the critical value =α/2,= \alpha / 2 ,=α/2, (b) find the critical value tα/2∘t _ { \alpha / 2 } { } ^ { \circ }tα/2​∘ 99 % ; n=17 ; α\alphaα is unknown; population appears to be normally distributed.

Identify the distribution that applies to the following situation: In constructing a confidence interval of μ\muμ , you have 50 sample values and they appear to be from a population with a skewed distribution. The population standard deviation is not known.

Of 380 randomly selected medical students, 21 said that they planned to work in a rural community. Find a 95 % confidence interval for the true proportion of all medical students who plan to work in a rural community.

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p . n=195, x=162 ; 95 % confidence

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ\muμ Assume that the population has a normal distribution. n=30 , xˉ=84.6\bar { x } = 84.6xˉ=84.6 s=10.5,90 % confidence

Define in as clear language as possible how a 95% confidence interval can be used for hypothesis tests.

A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 90 % confidence interval for the mean score, μ\muμ , of all students taking the test?

Express the confidence interval (0.432,0.52) in the form of p^±E\hat { p } \pm \mathrm { E }p^​±E

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

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

Fifty people are selected randomly from a certain population and it is found that 12 people in the sample are over six feet tall. What is the best point estimate of the proportion of people in the population who are over 6 feet tall?

Introduction to Statistics

Exploring Data With Tables and Graphs

Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Goodness-Of-Fit and Contingency Tables

Analysis of Variance

Nonparametric Tests

Statistical Process Control

Filters

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

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

Do one of the following, as appropriate: (a) Find the critical value $= \alpha / 2 ,$ (b) find the critical value $t _ { \alpha / 2 } { } ^ { \circ }$ 99 % ; n=17 ; $\alpha$ is unknown; population appears to be normally distributed.

Identify the distribution that applies to the following situation: In constructing a confidence interval of $\mu$ , you have 50 sample values and they appear to be from a population with a skewed distribution. The population standard deviation is not known.

Use the given degree of confidence and sample data to construct a confidence interval for the population mean $\mu$ Assume that the population has a normal distribution. n=30 , $\bar { x } = 84.6$ s=10.5,90 % confidence

A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 90 % confidence interval for the mean score, $\mu$ , of all students taking the test?

Express the confidence interval (0.432,0.52) in the form of $\hat { p } \pm \mathrm { E }$

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