Project #21702 - STATISTICS

1. ____________ ______________ is the value of a statistic that estimates the value of a parameter.

 

A. CRITICAL VALUE

 

B. CONFIDENCE LEVEL

 

C. POINT ESTIMATE

 

D. CONFIDENCE INTERVAL

 

 

 

2. Why does the margin of error increases as the level of confidence increases?

 

 

 

A. The margin of error increases as the level of confidence increases because the smaller the expected proportion of intervals that will contain the parameter, the larger the margin of error.

 

 

 

B. The margin of error increases as the level of confidence increases because, as the level of confidence increases, the sample size n increases.

 

 

 

C. The margin of error increases as the level of confidence increases because of the law of large numbers.

 

 

 

D. The margin of error increases as the level of confidence increases because the larger the expected proportion of intervals that will contain the parameter, the larger the margin of error.

 

 

 

3. Why does the margin of error decreases as the sample size n increases?

 

 

 

A. The margin of error decreases as the sample size n increases because the difference between the statistic and the parameter increases. This is a consequence of the Law of Larger Numbers.

 

 

 

B. The margin of error decreases as the sample size n increases because the difference between the statistic and the parameter decreases. This is a consequence of the Law of Larger Numbers.

 

 

 

C. The margin of error decreases as the sample size n increases because the critical value decreases as n increases.

 

 

 

D. The margin of error decreases as the sample size n increases because the confidence level becomes smaller as n increases.

 

 

 

4. Compute the critical value z a/2 that corresponds to 83% of confidence.

 

z a/2=____

 

(Round to two decial places as needed)

 

 

 

5. Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided.

 

 

 

Lower bound= 0.330, upper bound= 0.900, n=1000

 

 

 

The point estimate of the population proportion is ____

 

(Round to the nearest thousandth as needed)

 

 

 

The margin of error is ____

 

(Round to the nearest thousandth as needed)

 

The number of individuals in the sample with the specified characteristic is____

 

(round to the nearest integer as needed)

 

 

 

6. If the consequences of making a Type I error are severe, would you choose the level of significance, a, to equal 0.01, 0.05, or 0.10?

 

 

 

Choose the correct answer

 

A. 0.001

 

B. 0.05

 

C. 0.10

 

 

 

7. Determine whether the following statement is true or false.

 

Sample evidence can prove that a null hypothesis is true.

 

A. True

 

B. False

 

 

 

8. A null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed or two-tailed. What parameter is being tested?

 

H0: p=0.3

 

H1: p<0.3

 

 

 

What type of test is being conducted in this problem?

 

A. Left-sailed test

 

B. Two-tailed test

 

C. Right-tailed test

 

 

 

What parameter is being tested?

 

 

 

A. Population standard deviation

 

B. Population mean

 

C. Population proportion

 

 

 

9. (a) Determine the null and alternative hypotheses, (b) explain what it would mean to make a type I error, and (c) explain what it would mean to make a type II error.

 

Three years ago, the mean price of a single-family home was $243,719. A real estate broker believes that the mean price has decreased since then.

 

 

 

(a) Which of the following is the hypothesis test to be conducted?

 

A. Ho: μ =243,719; H1: μ < $243,719

 

B. Ho: μ= $243,719; H1; μ > $243,179

 

C. Ho μ= $243,719; H1; μ ≠ $243,719

 

 

 

(b) Which of the following is a Type I error?

 

A. The broker fails to reject the hypothesis that the mean price is $243,719, when the true mean price is less than $243,719.

 

B. The broker rejects the hypothesis that the mean price is $243,719, when the true mean prixe is less than $243,719

 

C. The broker rejects the hypothesis that the mean price is $243,719, when it is the true mean cost.

 

 

 

(c) Which of the following is a Type II error?

 

A. The broker fails to reject the hypothesis that the mean price is $243,719 when it is the true mean cost.

 

B. The broker fails to reject the hypothesis that the mean price is $243,719, when the true mean price is less that $243,719

 

C. The broker rejects the hypothesis that the mean is $243,719, when it is the true mean cost.

 

 

 

10. Test the hypothesis using the classical approach and the P-value approach.

 

H0: p=0.90 versus H1: p<0.90

 

n=150, x=125, a=0.05

 

 

 

(a) Perform the test using the classical approach. Choose the correct answer below.

 

 

 

A. Do not reject the null hypothesis

 

B. Reject the null hypothesis

 

C. There is not enough information to test the hypothesis

 

 

 

(b) Perform the test using P-value.

 

P-value=________ (Round to four decimal places as needed)

 

 

 

Choose the correct answer below.

 

 

 

A. There is not enough information to test the hypothesis

 

B. Do not reject the null hypothesis

 

C. Reject the null hypothesis

 

 

 

11. To test Ho: μ=40 versus H1: μ<40, a random sample of size n=22 is obtained from a population that is known to be normally distributed. Complete the parts (a) through (d) below.

 

(a) If _ =37.3 and s= 13.7, compute the test statistic.

 

X

 

t0=___ (Round to three decimal places as needed)

 

 

 

(b) If the researcher decides to test this hypothesis at the a= 0.05 level of significance, determine the critical value (s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table.

 

 

 

ta=______(Round to three decimal places. Use a comma to separate answers as needed)

 

 

 

(c) Draw a t-distribution that depicts the critical region.

 

DRAW HERE.

 

 

 

(d) Will the researcher reject the null hypothesis?

 

 

 

A. Yes, because the test statistic does not fall in the critical region.

 

B. No, because the test statistic fall in the critical region.

 

C. No, because the test statistic does not fall in the critical region

 

D. Yes, because the test statistic fall in the critical region.

 

 

 

12. Determine the t-value in each of the case.

 

 

 

(a) Find the t-value such that the area in the right is 0.01 with 5 degrees of freedom.

 

____( round to three decimal places as needed)

 

(b) Find the t-value such that the area in the right tail is 0.20 with 11 degrees of freedom. ____( round to three decial places as needed)

 

 

 

(c) Find the t-value such that the area left of the t-value is 0.05 with 26 degrees of freedom.

 

(hint. Use symmetry) _____(Round to three decimal places as needed)

 

 

 

(d) Find the critical t-value that corresponds to 95% confidence. Assume 11 degrees of freedom.

 

_____( Round to three decimal places as needed)

 

 

 

13. A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, __, is found to be 115, and the sample standard deviation, s, is found to be 10.

 

X

 

(a) construct a 98% confidence interval about μ if the sample size, n, is 15.

 

(___,___) (use ascending order. Round to one decimal place as needed.)

 

 

 

(b) Construct a 98% confidence interval about μif the sample size, n, is 24.

 

(___,___) (Use ascending order. Round to one decimal place as needed.)

 

 

 

How does increasing the sample size affect the margin of error, E?

 

A. As the sample size increases, the margin of error increases.

 

B. As the sample size increases, the margin of error decreases.

 

C. As the sample size increases, the margin of error stays the same.

 

 

 

(c) Construct a 99% confidence interval about μif the sample size, n, is 15.

 

(___,___)

 

(Use the ascending order. Round to one decimal place as needed.)

 

 

 

Compare the results to those obtained in part (a). How does increasing the level confidence affect the size of the margin of error, E?

 

A. As the percent confidence increases, the size of interval increases.

 

B. As the percent confidence increases, the size of the interval stays the same.

 

C. As the percent confidence increases, the size of the interval decreases.

 

 

 

(d) Could we have computer the confidence intervals in parts (a)-(c) if the population had not been normally distributed?

 

A. Yes, the population does not need to be normally distributed.

 

B. No, the population needs to be normally distributed,

 

C. No, the population does not need to be normally distributed,

 

D. Yes, the population needs to be normally distributed.

 

 

 

14. Based on interview with 95 SARS patients, researchers found that the mean incubation period was 4.8 days, with a standard deviation of 14.4 days. Based on this information, construct a 95% confidence interval for the mean incubation period of the SSARS virus. Interpret the interval.

 

 

 

The lower bound is______ days (Round to the decimal places as needed.)

 

The upper bound is ______days. (Round to two decimal places as needed.)

 

Interpret the interval. Choose the coorect answer below.

 

 

 

A. There is a 95% probability that the mean incubation period lies between the lower and upper bounds of the interval.

 

B. There is a 95% confidence that the mean incubation period lies between the lower and upper bounds of the interval.

 

C. There is a 95% confidence that the mean incubation period is greater than the upper bound of the interval.

 

D. There is a 95% confidence that the mean incubation period is less than the lower bound of the interval.

 

 

 

15. Compute the critical value z a/2 that corresponds to q 98% of confidence.

 

Za/2=____( round to two decimal places as needed.)

 

 

 

16.
A group of researchers studied the effect of global environmental change on grazing lands. Their article reported the results of 171 different hypothesis tests. Of these tests, 4 were determined to be statistically significant at the 0.05 level.

 

  1. When constructing and implementing hypothesis tests, what reasoning is used behind the statement of the null and alternative hypotheses?

  2. Why are hypothesis tests set up in this way?

  3. For each of the tests, what was the probability of committing a type I error? Explain.

  4. Based on this information, what conclusions might be drawn?

 

Subject Mathematics
Due By (Pacific Time) 01/30/2014 12:00 am
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