Deck 7: Estimates and Sample Size

Question 1

Bert constructed a confidence interval to estimate the mean weight of students in his class.
The population was very small - only 30. Ruth constructed a confidence interval for the mean weight of all adult males in the city. She based her confidence interval on a very small sample of only 5. Which confidence interval is likely to give a better estimate of the mean it is estimating? Which is likely to be more of a problem, a small sample or a small population?

Answer 1

Bert's confidence interval is likely to give a better estimate. A small sample is more likely to be a problem than a small population.

Question 2

When determining the sample size for a desired margin of error, the formula is $\mathrm { n } = \frac { [ \mathrm { z } \alpha / 2 ] ^ { 2 } \hat { \mathrm { p }}\hat { \mathrm { q } } } { \mathrm { E } ^ { 2 } }$ . Based on this formula, discuss the fact that sample size is not dependent on the population size; that is, it is not necessary to sample a particular percent of the population.

Answer 2

As shown in the formula, the appropriate sample size is dependent on the appropriate z score, the sample proportion, and the margin of error, not on N, the population size.

Question 3

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

Answer 3

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 4

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?

Question 5

When determining the sample size needed to achieve a particular error estimate you need to know ?. What are two methods of estimating ? if ? is unknown?

Question 6

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

Question 7

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?

Question 8

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

Question 9

Describe the steps for finding a confidence interval.

Question 10

Complete the table to compare z and t distributions.

Question 11

Interpret the following 95% confidence interval for mean weekly salaries of shift managers at Guiseppe's Pizza and Pasta. 325.80 < µ < 472.30

Question 12

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

Question 13

A researcher is interested in estimating the proportion of voters who favor a tax on e-commerce. Based on a sample of 250 people, she obtains the following 99% confidence interval for the population proportion, $\mathrm { p } : 0.113 < \mathrm { p } < 0.171$ Which of the statements below is a valid interpretation
Of this confidence interval?

A) If 100 different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, exactly 99 of these confidence intervals would contain the true value of p.
B) If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, 99% of the time the true value of p would lie between 0.113 and 0.171.
C) There is a 99% chance that the true value of p lies between 0.113 and 0.171.
D) If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, in the long run 99% of the confidence intervals would contain the true value of p.

Question 14

What assumption about the parent population is needed to use the t distribution to compute the margin of error?

Question 15

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?

Question 16

What is the best point estimate for the population proportion? Explain why that point estimate is best.

Question 17

Explain how confidence intervals might be used to make decisions. Give an example to clarify your explanation.

Question 18

When determining sample size we need to know $\hat { \mathrm { p } }$ . If we have no prior information, what are two methods that can be used?

Question 19

Question 20

Explain the difference between descriptive and inferential statistics.

Question 21

50 people are selected randomly from a certain population and it is found that 18 people in the sample are over 6 feet tall. What is the point estimate of the proportion of people in the population who are over 6 feet tall?

A) 0.50
B) 0.36
C) 0.64
D) 0.23

Question 22

A $99 \%$ confidence interval (in inches) for the mean height of a population is $66.2 < \mu < 67.6$ . This result is based on a sample of size 144 . Construct the $95 \%$ confidence interval. (Hint: you will first need to find the sample mean and sample standard deviation).

A) $66.2$ in $< \mu < 67.6$ in.
B) $66.0$ in $< \mu < 67.8$ in.
C) $66.3$ in $< \mu < 67.5$ in.
D) $66.4$ in $< \mu < 67.4 \mathrm { in }$ .

Question 23

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.

-A sociologist develops a test to measure attitudes towards public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4.
Construct the 95% confidence interval for the mean score of all such subjects.

A) $74.6 < \mu < 77.8$
B) $67.7 < \mu < 84.7$
C) $64.2 < \mu < 88.2$
D) $69.2 < \mu < 83.2$

Question 24

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.

-Test scores: $\mathrm { n } = 79 , \overline { \mathrm { x } } = 65.0 , \sigma = 5.0 ; 98 \%$ confidence

A) $64.1 < \mu < 65.9$
B) $63.9 < \mu < 66.1$
C) $63.5 < \mu < 66.5$
D) $63.7 < \mu < 66.3$

Question 25

The Bide-a-While efficiency hotel, which caters to business workers who stay for extended periods of time (weeks or months), offers room service. In a small study of 35 randomly selected room service orders, the 95% confidence interval for mean delivery time for room service is $24.8 < \mu < 29.6$ minutes. The marketing director is trying to determine if she can advertise "room service in under 30 minutes, or the order is free." How would you advise her?

Question 26

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 group of 64 randomly selected students have a mean score of $38.6$ with a standard deviation of $4.9$ on a placement test. What is the $90 \%$ confidence interval for the mean score, $\mu$ , of all students taking the test?

A) $37.4 < \mu < 39.8$
B) $37.2 < \mu < 40.0$
C) $37.6 < \mu < 39.6$
D) $37.0 < \mu < 40.2$

Question 27

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

Question 28

Use the given data to find the minimum sample size required to estimate the population proportion.

-Margin of error: 0.018; confidence level: $99 \% ; \hat { \mathrm { p } } \text { and } \hat { \mathrm { q } } \text { unknown }$

A) 4966
B) 4114
C) 7116
D) 5117

Question 29

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

- $\mathrm { n } = 110 , \mathrm { x } = 68 ; 88 \%$ confidence

A) $0.545 < p < 0.691$
B) $0.541 < p < 0.695$
C) $0.542 < p < 0.694$
D) $0.546 < p < 0.690$

Question 30

In constructing a confidence interval for $\sigma$ or $\sigma ^ { 2 }$ , a table is used to find the critical values $\chi _ { L } ^ { 2 }$ and $\chi \underset { R } { 2 }$ for values of $n \leq 101$ . For larger values of $n , \chi _ { L } ^ { 2 }$ and $\chi { } _ { \mathrm { R } } ^ { 2 }$ can be approximated by using the following formula: $\chi ^ { 2 } = \frac { 1 } { 2 } [ \pm \mathrm { z } \alpha / 2 + \sqrt { 2 \mathrm { k } - 1 } ] ^ { 2 }$ where $\mathrm { k }$ is the number of degrees of freedom and $\mathrm { z } \alpha / 2$ is the critical z score. Construct the $90 \%$ confidence interval for $\sigma$ using the following sample data: a sample of size $\mathrm { n } = 234$ yields a mean weight of $155 \mathrm { lb }$ and a standard deviation of $26.0 \mathrm { lb }$ . Round the confidence interval limits to the nearest hundredth.

A) $24.13 \mathrm { lb } < \sigma < 28.11 \mathrm { lb }$
B) $24.18 \mathrm { lb } < \sigma < 28.18 \mathrm { lb }$
C) $24.57 \mathrm { lb } < \sigma < 27.67 \mathrm { lb }$
D) $23.86 \mathrm { lb } < \sigma < 28.63 \mathrm { lb }$

Question 31

A radio show host asked people to call in and say whether they support new legislation to promote cleaner sources of energy. Based on this sample, she constructed a confidence interval to estimate the proportion of all listeners to her show who support the legislation.
Is the confidence interval likely to give a good estimate of the proportion of her listeners who support the legislation?

Question 32

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?

Question 33

Use the given data to find the minimum sample size required to estimate the population proportion.

-Margin of error: 0.008; confidence level: 99%; from a prior study, $\hat{p}$ is estimated by 0.208.

A) 9889
B) 15,361
C) 137
D) 17,068

Question 34

Define a point estimate. What is the best point estimate for ?

Question 35

Mark wanted to estimate the mean number of years of education of adults in his city. He waited outside a public library and interviewed every tenth adult leaving. Based on this sample, he constructed a confidence interval for the mean number of years of education of adults in the city. Do you think this confidence interval will give a good estimate? Why or why not?

Question 36

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

Question 37

Define confidence interval and degree of confidence. Make up an example of a confidence interval and interpret the result.

Question 38

Of 366 randomly selected medical students, 27 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.

A) $0.0513 < p < 0.0962$
B) $0.0470 < p < 0.101$
C) $0.0419 < p < 0.106$
D) $0.0386 < p < 0.109$

Question 39

Use the given data to find the minimum sample size required to estimate the population proportion.

-Margin of error: $0.028$ ; confidence level: $99 \% ; \hat { \mathrm { p } }$ and $\hat { \mathrm { q } }$ unknown

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

Question 40

Identify the correct distribution (z, t, or neither) for each of the following. $$\begin{array} { | l | l | l | l | } \hline \text { Sample Size } & \begin{array} { l } \text { Standard } \\\text { deviation }\end{array} & \begin{array} { l } \text { Shape of the } \\\text { distribution }\end{array} & \text { z or t or neither } \\\hline n = 35 & s = 4.5 & \text { Somewhat skewed } & \\\hline n = 20 & s = 4.5 & \text { Bell shaped } & \\\hline n = 25 & \sigma = 4.5 & \text { Bell shaped } & \\\hline n = 20 & \sigma = 4.5 & \text { Extremely skewed } & \\\hline\end{array}$$

Question 41

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.

- $90 \% \text { confidence; } n = 430 , x = 80$

A) 0.0386
B) 0.0368
C) 0.0331
D) 0.0309

Question 42

A newspaper article about the results of a poll states: "In theory, the results of such a poll, in 99 cases out of 100 should differ by no more than 2 percentage points in either direction from what would have been obtained by interviewing all voters in the United States." Find the sample size suggested by this statement.

A) 2402
B) 4145
C) 165
D) 3394

Question 43

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.

- $90 \% ; \mathrm { n } = 10 ; \sigma$ is unknown; population appears to be normally distributed.

A) $\mathrm { t } _ { \alpha / 2 } = 1.833$
B) $\mathrm { z } _ { \alpha / 2 } = 2.262$
C) $\mathrm { t } _ { \alpha / 2 } = 1.812$
D) $\mathrm { z } _ { \alpha / 2 } = 1.383$

Question 44

In a clinical test with 8900 subjects, 4450 showed improvement from the treatment. Find the margin of error for the 99% confidence interval used to estimate the population proportion.

A) 0.00780
B) 0.0137
C) 0.0120
D) 0.0104

Question 45

Use the given information to find the minimum sample size required to estimate an unknown population mean µ.

- $\text { Margin of error: } \$ 134 \text {, confidence level: } 95 \% , \sigma = \$ 575$

A) 71
B) 62
C) 50
D) 100

Question 46

Use the given data to find the minimum sample size required to estimate the population proportion.

- $\text { Margin of error: } 0.008 \text {; confidence level: } 99 \% ; \hat { \mathrm { p } } \text { and } \hat { \mathrm { q } } \text { unknown }$

A) 25,901
B) 15,900
C) 26,024
D) 25,894

Question 47

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation ?.
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.

-Weights of men: $90 \%$ confidence; $\mathrm { n } = 14 , \overline { \mathrm { x } } = 154.8 \mathrm { lb } , \mathrm { s } = 11.1 \mathrm { lb }$

A) $8.7 \mathrm { lb } < \sigma < 14.3 \mathrm { lb }$
B) $8.2 \mathrm { lb } < \sigma < 15.6 \mathrm { lb }$
C) $9.0 \mathrm { lb } < \sigma < 2.7 \mathrm { lb }$
D) $8.5 \mathrm { lb } < \sigma < 16.5 \mathrm { lb }$

Question 48

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.

-The principal randomly selected six students to take an aptitude test. Their scores were: $\begin{array} { l l l l l l } 81.4 & 78.6 & 71.3 & 77.8 & 76.9 & 77.7 \end{array}$
Determine a $90 \%$ confidence interval for the mean score for all students.

A) $80.11 < \mu < 74.45$
B) $80.01 < \mu < 74.55$
C) $74.55 < \mu < 80.01$
D) $74.45 < \mu < 80.11$

Question 49

Solve the problem. Round the point estimate to the nearest thousandth.
364 randomly selected light bulbs were tested in a laboratory, 124 lasted more than 500 hours. Find a point estimate of the proportion of all light bulbs that last more than 500 hours.

A) 0.254
B) 0.659
C) 0.338
D) 0.341

Question 50

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation ?.
Assume that the population has a normal distribution. Round the confidence interval limits to one more decimal place than is used for the original set of data.

-The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were:
$$\begin{array} { c c c c c } 7 & 9 & 13 & 6 & 7 \\5 & 9 & 5 & 15 & 13\end{array}$$
Find a $95 \%$ confidence interval for the population standard deviation $\sigma$ .

A) $0.8 \mathrm {~min} < \sigma < 2.4 \mathrm {~min}$
B) $2.4 \mathrm {~min} < \sigma < 6.0 \mathrm {~min}$
C) $2.5 \mathrm {~min} < \sigma < 6.0 \mathrm {~min}$
D) $2.5 \mathrm {~min} < \sigma < 6.6 \mathrm {~min}$

Question 51

Use the given data to find the minimum sample size required to estimate the population proportion.

-Margin of error: $0.09$ ; confidence level: $95 \%$ ; from a prior study, $\hat { \mathrm { p } }$ is estimated by the decima equivalent of $87 \%$ .

A) 5
B) 48
C) 54
D) 162

Question 52

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

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

Question 53

Use the given information to find the minimum sample size required to estimate an unknown population mean µ.

-How many students must be randomly selected to estimate the mean weekly earnings of students at one college? We want 95% confidence that the sample mean is within $2 of the population mean, and the population standard deviation is known to be $10.

A) 136
B) 97
C) 68
D) 85

Question 54

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

- $\mathrm { n } = 150 , \mathrm { x } = 54 ; 90 \%$ confidence

A) $0.299 < p < 0.421$
B) $0.296 < p < 0.424$
C) $0.298 < p < 0.422$
D) $0.294 < p < 0.426$

Question 55

Use the given information to find the minimum sample size required to estimate an unknown population mean µ.

- $\text { Margin of error: } \$ 136 \text {, confidence level: } 99 \% , \sigma = \$ 584$

A) 62
B) 123
C) 50
D) 71

Question 56

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.

-A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $297.29. Find a 98% confidence interval for the true mean checking account balance for local customers.

A) $\$ 492.52 < \mu < \$ 835.76$
B) $\$ 493.71 < \mu < \$ 834.57$
C) $\$ 453.59 < \mu < \$ 874.69$
D) $\$ 455.65 < \mu < \$ 872.63$

Question 57

Use the given data to find the minimum sample size required to estimate the population proportion.

- $\text { Margin of error: 0.009; confidence level: } 99 \% ; \hat { \mathrm { p } } \text { and } \hat { \mathrm { q } } \text { unknown }$

A) 20,465
B) 21,442
C) 9642
D) 19,566

Question 58

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.

-90% confidence; the sample size is 1410, of which 40% are successes

A) 0.0167
B) 0.0267
C) 0.0256
D) 0.0215

Question 59

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.

-95% confidence; the sample size is 6100, of which 40% are successes

A) 0.00923
B) 0.0141
C) 0.0123
D) 0.0162

Question 60

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.

- $95 \% \text { confidence; } \mathrm { n } = 470 , \mathrm { x } = 50$

A) 0.0251
B) 0.0335
C) 0.0293
D) 0.0279

Question 61

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

-Of 80 adults selected randomly from one town, 67 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance.

A) $0.741 < \mathrm { p } < 0.934$
B) $0.731 < \mathrm { p } < 0.944$
C) $0.757 < p < 0.918$
D) $0.770 < p < 0.905$

Question 62

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 random sample of 108 light bulbs had a mean life of $\bar { x } = 547$ hours with a standard deviation of $\sigma = 36$ hours. Construct a $90 \%$ confidence interval for the mean life, $\mu$ , of all light bulbs of this type.

A) $541 \mathrm { hr } < \mu < 553 \mathrm { hr }$
B) $538 \mathrm { hr } < \mu < 556 \mathrm { hr }$
C) $539 \mathrm { hr } < \mu < 555 \mathrm { hr }$
D) $540 \mathrm { hr } < \mu < 554 \mathrm { hr }$

Question 63

Use the given information to find the minimum sample size required to estimate an unknown population mean µ.

-How many women must be randomly selected to estimate the mean weight of women in one age group. We want 90% confidence that the sample mean is within 2.8 lb of the population mean, and the population standard deviation is known to be 27 lb.

A) 358
B) 253
C) 252
D) 250

Question 64

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.

-Thirty randomly selected students took the calculus final. If the sample mean was 75 and the standard deviation was 13.2, construct a 99% confidence interval for the mean score of all students.

A) $68.38 < \mu < 81.62$
B) $70.91 < \mu < 79.09$
C) $68.36 < \mu < 81.64$
D) $69.07 < \mu < 80.93$

Question 65

The amounts (in ounces) of juice in eight randomly selected juice bottles are:
$\begin{array} { l l l l l } 15.3 & 15.3 & 15.7 & 15.7\\15.3&15 .9&15 .3&15 .9\\ \end{array}$
Construct a $98 \%$ confidence interval for the mean amount of juice in all such bottle

A) $15.83 \mathrm { oz } < \mu < 15.27 \mathrm { oz }$
B) $15.93 \mathrm { oz } < \mu < 15.17 \mathrm { oz }$
C) $15.27 \mathrm { oz } < \mu < 15.83 \mathrm { oz }$
D) $15.17 \mathrm { oz } < \mu < 15.93 \mathrm { oz }$

Question 66

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation ?.
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.

-A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4.
Construct the 95% confidence interval for the standard deviation, ?, of the scores of all subjects.

A) $16.9 < \sigma < 29.3$
B) $17.5 < \sigma < 27.8$
C) $16.6 < \sigma < 28.6$
D) $17.2 < \sigma < 27.2$

Question 67

Use the given data to find the minimum sample size required to estimate the population proportion.

-Margin of error: 0.04; confidence level: 99%; from a prior study, $\hat { p }$ is estimated by 0.14.

A) 499
B) 20
C) 289
D) 599

Question 68

Express the confidence interval using the indicated format.

-Express the confidence interval $0.307 \pm 0.058$ in the form of $\hat { p } - \mathrm { E } < \mathrm { p } < \hat { \mathrm { p } } + \mathrm { E }$ .

A) $0.278 < p < 0.336$
B) $0.307 < p < 0.365$
C) $0.249 < p < 0.307$
D) $0.249 < p < 0.365$

Question 69

Find the critical value $\mathrm { z } _ { \alpha / 2 }$ that corresponds to a 98% confidence level.

A) 2.575
B) 2.33
C) 2.05
D) 1.75

Question 70

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.

-99% confidence; the sample size is 1180, of which 45% are successes

A) 0.0297
B) 0.0284
C) 0.0337
D) 0.0373

Question 71

Find the critical value $\chi _ { \mathrm { R } } ^ { 2 }$ corresponding to a sample size of 7 and a confidence level of 90 percent.

A) 1.635
B) 12.592
C) 18.548
D) 16.812

Question 72

Express the confidence interval using the indicated format.

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

A) $0.67 \pm 0.05$
B) $0.62 \pm 0.1$
C) $0.62 \pm 0.05$
D) $0.67 \pm 0.1$

Question 73

$\text { Find } z _ { \alpha / 2 } \text { for } \alpha = 0.06$

A) 1.88
B) 1.555
C) 1.96
D) 2.75

Question 74

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.

-Test scores: $\mathrm { n } = 102 , \overline { \mathrm { x } } = 77.4 , \sigma = 6.5 ; 99 \%$ confidence

A) $76.1 < \mu < 78.7$
B) $75.7 < \mu < 79.1$
C) $75.9 < \mu < 78.9$
D) $76.3 < \mu < 78.5$

Question 75

The following confidence interval is obtained for a population proportion, $p : 0.686 < p < 0.712$ . Use these confidence interval limits to find the point estimate, $\hat {\mathrm { p }}$ .

A) 0.699
B) 0.704
C) 0.686
D) 0.694

Question 76

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.

- $\mathrm { n } = 10 , \overline { \mathrm { x } } = 12.7 , \mathrm {~s} = 3.7,95 \%$ confidence

A) $10.07 < \mu < 15.33$
B) $10.05 < \mu < 15.35$
C) $10.09 < \mu < 15.31$
D) $10.56 < \mu < 14.84$

Question 77

$\mathrm { n } = 12 , \overline { \mathrm { x } } = 21.9 , \mathrm {~s} = 4.0,99 \%$ confidence

A) $18.24 < \mu < 25.56$
B) $18.76 < \mu < 25.04$
C) $18.31 < \mu < 25.49$
D) $18.33 < \mu < 25.47$

Question 78

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.

-A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 198 milligrams with $\mathrm { s } = 10.5$ milligrams. Construct a $95 \%$ confidence interval for the true mean cholesterol content of all such eggs.

A) $191.3 \mathrm { mg } < \mu < 204.7 \mathrm { mg }$
B) $191.4 \mathrm { mg } < \mu < 204.6 \mathrm { mg }$
C) $191.2 \mathrm { mg } < \mu < 204.8 \mathrm { mg }$
D) $192.6 \mathrm { mg } < \mu < 203.4 \mathrm { mg }$

Question 79

Use the given data to find the minimum sample size required to estimate the population proportion.

-Margin of error: 0.008; confidence level $95 \% ; \hat { \mathrm { p } } \text { and } \hat { \mathrm { q } } \text { unknown }$

A) 15,007
B) 15,098
C) 14,488
D) 5045

Question 80

Find the chi-square value $x _ { L } ^ { 2 }$ corresponding to a sample size of 4 and a confidence level of 98 percent.

A) 0.216
B) 9.348
C) 0.115
D) 11.345