# Statistics

The t distribution is a continuous distribution (Points : 6)

True

False

2. A confidence interval for a population mean (Points : 6)

estimates the population range

estimates a likely interval for a population mean

estimates a likelihood or probability

estimates the population standard deviation

3. A 95% confidence interval infers that the population mean (Points : 6)

is between 0 and 100%

is within ± 1.96 standard deviations of the sample mean

is within ± 1.96 standard errors of the sample mean

is too large

4. What is the interval within which a population parameter is expected to lie? (Points : 6)

Sample

Expected Value

Standard Deviation

Confidence Interval

5. Please choose the appropriate answer for the cut-off/critical value ranges to go in the blank for each question (5-8):

One-Tailed

Two-Tailed

95% (or .05) significance level Question 5.

99% (or .01) significance level

(Points : 6)

-2.58 and 2.58

-1.65 or 1.65

-1.96 and 1.96

-2.33 or 2.33

6. Please choose the appropriate answer for the cut-off/critical value ranges to go in the blank for each question (5-8):

One-Tailed

Two-Tailed

95% (or .05) significance level

Question 6.

99% (or .01) significance level

(Points : 6)

-2.58 and 2.58

-1.65 or 1.65

-1.96 and 1.96

-2.33 or 2.33

7. Please choose the appropriate answer for the cut-off/critical value ranges to go in the blank for each question (5-8):

One-Tailed

Two-Tailed

95% (or .05) significance level

99% (or .01) significance level

Question 7.

(Points : 6)

-2.58 and 2.58

-1.65 or 1.65

-1.96 and 1.96

-2.33 or 2.33

8. Please choose the appropriate answer for the cut-off/critical value ranges to go in the blank for each question (5-8):

One-Tailed

Two-Tailed

95% (or .05) significance level

99% (or .01) significance level

Question 8.

(Points : 6)

-2.58 and 2.58

-1.65 or 1.65

-1.96 and 1.96

-2.33 or 2.33

9. To determine the size of a sample, the standard deviation of the population must be estimated by either taking a pilot survey or by approximating it based on knowledge of the population. (Points : 6)

True

False

10. The t distribution is based on the assumption that the population of interest is normal or nearly normal. (Points : 6)

True

False

11. Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000 with a standard deviation of $2,500

What is the best point estimate of the population mean?

(Points : 6)

$25,000

$2,500

$400

$62.50

12. Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000 with a standard deviation of $2,500.

What is the 95% confidence interval for the mean salary of all graduates from the English Department?

(Points : 6)

[$22,500, $27,500]

[$24,755, $25,245]

[$24,988, $25,012]

[$24,600, $25,600]

13. Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000 with a standard deviation of $2,500.

What do the confidence interval results mean?

(Points : 6)

The population mean is in the interval

The population mean is not in the interval

The likelihood that any confidence interval based on a sample of 400 graduates will contain the population mean is 0.95

There is a 5% chance that the computed interval does not contain the population mean.

14. The proportion of junior executives leaving large manufacturing companies within three years is to be estimated within 3 percent. The 0.95 degree of confidence is to be used. A study conducted several years ago revealed that the percent of junior executives leaving within three years was 21. To update this study, the files of how many junior executives should be studied?

(Points : 6)

594

612

709

897

15.

7. There are 2,000 eligible voters in a precinct. 500 of the voters are selected at random and asked to indicate whether they planned to vote for the Democratic incumbent or the Republican challenger. Of the 500 surveyed, 350 said they were going to vote for the Democratic incumbent. Using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the Democratic incumbent?

(Points : 6)

0.647 and 0.753

0.612 and 0.712

0.397 and 0.797

0.826 and 0.926

16. In opening a new Curves, the company advertises that, while on the Curves diet and workout routine, new members lose an average of 10 pounds in the first two weeks with a population standard deviation of 2.8 pounds. A random sample of 50 women who joined the program revealed a mean loss of 9 pounds. At a .05 level of significance, use the steps in hypothesis testing to see if we can conclude that those joining Curves on average will lose less than 10 pounds.

Is this a one-tailed or two-tailed test?

(Points : 5)

One Tailed

Two Tailed

17. In opening a new Curves, the company advertises that, while on the Curves diet and workout routine, new members lose an average of 10 pounds in the first two weeks with a population standard deviation of 2.8 pounds. A random sample of 50 women who joined the program revealed a mean loss of 9 pounds. At a .05 level of significance, use the steps in hypothesis testing to see if we can conclude that those joining Curves on average will lose less than 10 pounds.

What is the cut-off (critical) value?

(Points : 5)

+/- 1.65

+/- 1.96

+/- 2.33

+/- 2.58

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Sufficiency and Order Statistics

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the uniform distribution over the closed interval [-theta, theta ]

having pdf f(x; theta ) = (1/2(theta))I[-theta , theta ](x).

Argue that the mle of theta; equals theta;hat= max(-Y1, Yn).

Demonstrate that the mle theta;hat is a sufficient statistic for theta;.

Define at least two ancillary statistics for this distribution

See attachment for better symbol representation.

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