Question

Answer the question.

CHAPTER 8: ESTIMATION AND CONFIDENCE INTERVALS

1. As degrees of freedom increase, the t-distribution approaches the:

A. binomial distribution

B. exponential distribution

C. standard normal distribution

D. None of the above

2. Given a t-distribution with 14 degrees of freedom, the area left of - 1.761 is

A. 0.025

B. 0.05

C. 0.10

D. 0.90

E. None of the above

3. 100 samples of size fifty were taken from a population with population mean 72. The sample mean and sample standard deviation were recorded and the 95% confidence interval for the population mean was recorded for each sample. Of the 100 confidence intervals, how many would we expect to have 72 between the endpoints?

A. 0

B. 5

C. 95

D. 100

4. You are given a confidence interval for the population mean of 26 to 42. The sample mean used to construct this confidence interval was:

A. 1.96

B. 26

C. 34

D. Cannot be determined with the given information

5. A sample of five price/earnings ratios for companies in the Services sector follows. 15 11 14 17 12 A confidence interval for the population mean is requested. In order to construct the confidence interval one must assume:

A. that the sample came from a normal distribution

B. that the population standard deviation is known

C. No assumptions are needed

D. None of choices are correct

6. A sample of five price/earnings ratios for companies in the Services sector follows. 15 11 14 17 12 A confidence interval for the population mean is requested. Assuming that the sample comes from a normal population, the appropriate distribution used in constructing this confidence interval is the:

A. F

B. t

C. z

D. ? 2

E. None of the choices are correct

7. A sample of five price/earnings ratios for companies in the Services sector follows. 15 11 14 17 12 A confidence interval for the population mean is requested. Assuming that the sample comes from a normal population, the appropriate degrees of freedom used for this confidence interval is:

A. 2

B. 3

C. 4

D. 5

E. None of the choices are correct

8. A sample of five price/earnings ratios for companies in the Services sector follows. 15 11 14 17 12 A confidence interval for the population mean is requested. Assuming that the sample comes from a normal population, the 95% confidence interval is

A. 6.39 to 21.21

B. 9.77 to 26.63

C. 10.84 to 16.76

D. 11.71 to 15.89 E.

None of the choices are correct

9. A sample of size 36 is taken from a population with standard deviation of the population is 12. The sample mean is found to be 116. Construct a 95% confidence interval.

A. - 25.89 to 49.89

B. 95.63 to 136.37

C. 111.94 to 120.06

D. 112.08 to 119.92

E. None of the above

10. The useful life of a certain type of light bulb is known to have a standard deviation of σ = 40 hours. How large a sample should be taken if it is desired to have a margin of error of 10 hours or less at a 95% level of confidence?

A. 8

B. 37

C. 44

D. 62

E. None of the choices are correct

11. A random sample of 300 voters showed 47% in favor of a certain ballot proposal. A 90% confidence interval estimate for the population proportion of voters favoring the proposal is:

A. 0.38 to 0.56

B. 0.4226 to 0.5174

C. 0.4412 to 0.4988

D. 0.4136 to 0.5264

E. None of the above

12. In choosing a sample size for a public-opinion survey, what hypothesized value of the population proportion will lead to the largest sample size when the confidence level and the maximum sample error are specified?

A. p = .

1 B. p = .5

C. p = .99

D. The confidence level must be known before an answer can be given

Answer question 13 - 14 based on the information below: Restoran Lazatlah has 1500 retail outlets throughout the Sabah. The owner, Mr. Rashid, is evaluating a potential location for a new outlet, based in part, on the mean annual income of the individuals in the marketing are of the new location. A sample of size n = 50 was taken; the sample mean income is RM24,000. The population is not believed to be highly skewed. The population standard deviation is estimated to be RM3000, and the confidence coefficient to be used in the interval estimate is .90.

13. Compute the margin of error to the point of estimate:

A. RM543.91

B. RM697.91

C. RM24000 + RM543.91

D. RM24000 + RM697.91

14. What is the interval estimate of the population mean:

A. RM543.91

B. RM697.91

C. RM24000 + RM543.91

D. RM24000 + RM697.91 Answer question 15 - 17 based on the information below: Public Says is an online survey firm that is doing a research to identify the opinion of the people in the Republic of Wakanda on who they would vote for in the coming presidential election. There are only two competing candidates for the office, T’Challa and Erik Killmonger that From the data retrieved, 7300 out of 10000 online respondents who are registered voters favor T’Challa.

15 Based on 95% confidence interval, what is the proportion of the population that favors T’Challa:

A. 0.8 + 0.0248

B. 0.8 + 0.0208

C. 0.8 + 0.0277

D. Cannot be determined with the given information

16. How large is the sample needed if Public Says would like a .99 probability that the sample proportion is within + 0.01 of the population proportion:

A. 8656

B. 13,526

C. 15,277

D. 23,870

17. If the population proportion is unknown, what is the highest possible sample size recommended:

A. 8656

B. 13,526

C. 15,277

D. 23,870

Answer #1

1. C. standard normal distribution

Explanation: As degrees of freedom increases, the t-distribution
**approaches normality**. This means that the area
near the center increases while the area near the tails decreases.
When df decreases, the area near the center decreases while the
area near the tails increases.

2. B. 0.05

Explanation: R code-

> pt(- 1.761, df = 14, lower.tail = TRUE)

[1] 0.05002709

4. C. 34

Explanation: given a confidence interval for the population mean of 26 to 42. Since t distribution is symmetric, confidence interval is symetrically spread. So answer is (26+42)/2 = 34. Note that, here we assumed that the data is from Nornal distribution (or assymtotically). Otherwise is not possible.

5. A. that the sample came from a normal distribution.

6. B. t

Explanation: T = . Note that, T is the statistics to test the hypothesis.

Question 1.
Which of the following is the CORRECT interpretation of a 95%
confidence interval?
a) There is a 95% probability that the interval contains the
population value
b) There is a 95% chance that the true population value is
inside the interval
c) if we sampled from a population repeatedly and created
confidence intervals, 95% of those confidence intervals would
contain the population mean
d) We are 95% sure of the sample statistic
Question 2.
What is the mean...

sample of size 36, the 95% confidence interval for the
population mean is 64.90, 69.30. The sample mean is:
66.04
None of the choices is correct.
67.10
63.10

Calculate the appropriate confidence interval for:
a. the population mean, if the sample mean is 17, the sample
size is 25, and the sample variance is 6, 95% confidence
b. the population mean, if the sample mean is 75, the sample
size is 5, and the sample variance is 8, 90% confidence
c. the population variance, if the sample variance is 4.5, the
sample size is 6, and the confidence is 98%
d. recalculate part a for 90% confidence
e....

Question 4: Confidence Intervals: Each question is worth 7.5
marks: Total A. Suppose we know the population standard
deviation is 0.03. We have a sample size of 121. We also have a
sample proportion of 0.65 and a confidence interval of 90%. Find
the interval for the population proportion with 90% confidence
level? ________________________________ B. Suppose we know the
population standard deviation is 4. We have a sample size of 144.
We also have a sample mean of 55 and...

For this term, we will create confidence intervals to estimate a
population value using the general formula:
sample estimator +/- (reliability factor)(standard error
of the estimator)
Recall that the (reliability factor) x (standard error of the
estimator)= margin of error (ME) for the interval.
The ME is a measure of the uncertainty in our estimate of the
population parameter. A confidence interval has a width=2ME.
A 95% confidence interval for the unobserved population
mean(µ), has a confidence level =
1-α...

1. When constructing a confidence interval to estimate a
population proportion, what affects the size of the margin of
error?
A. The sample size
B. The sample proportion
C. The confidence level
D. All of the above affect the size of the margin of error
E. None of the above affect the size of the margin of error
2. What percentage of couples meet through online dating
apps? A survey of a random sample of couples finds that 12% say...

a. Compute the 95% and 99% confidence intervals on the mean
based on a sample mean of 50 and population standard deviation of
10, for a sample of size 15.
b. What percent of the 95% confidence intervals would you expect
to contain µ? What percent of the 95% confidence intervals would
you expect to contain x̅? What percent of the 95% confidence
intervals would you expect to contain 50?
c. Do you think that the intervals containing µ will...

1. Develop 90 %, 95 %, and 99% confidence intervals for
population mean (µ) when sample mean is 10 with the sample size of
100. Population standard deviation is known to be 5.
2. Suppose that sample size changes to 144 and 225. Develop
three confidence intervals again. What happens to the margin of
error when sample size increases?
3. A simple random sample of 400 individuals provides 100 yes
responses. Compute the 90%, 95%, and 99% confidence interval for...

The following questions ask you to construct and compare
a series of confidence intervals.
A. In a representative sample
of 30 students, the mean quiz score was 54 points with a standard
deviation of 2 points. Construct a 95% confidence interval to
estimate the mean quiz score in the population of all
students. [5 points]
B. In a representative sample
of 100 students, the mean quiz score was 54 points with a standard
deviation of 2 points. Construct a 95%...

1 - Which of the following statements is true regarding a 95%
confidence interval? Assume numerous large samples are taken from
the population.
a. In 95% of all samples, the sample proportion will fall within 2
standard deviations of the mean, which is the true proportion for
the population.
b. In 95% of all samples, the true proportion will fall within 2
standard deviations of the sample proportion.
c. If we add and subtract 2 standard deviations to/from the sample...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 18 minutes ago

asked 21 minutes ago

asked 28 minutes ago

asked 53 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago