Download (1) In real-world problems, the population standard deviation is often

(1) In real-world problems, the population standard deviation is often unknown.
A)
True
B)
False
(2) The objective of inferential statistics is to use the information contained in the sample data to increase our knowledge of the
population.
A)
True
B)
False
(3) The quality of an estimation procedure (or method) is greatly enhanced if the sample statistic is both less variable and unbiased.
A)
True
B)
False
(4) A point estimate for a parameter is a single number designed to estimate a quantitative parameter of a population, usually the
value of the corresponding sample statistic
A)
True
B)
False
(5) When estimating a population mean with a confidence interval estimate, then E is:
A)
equal to the level of confidence.
B)
one-half the width of the confidence interval.
C)
a multiple of the population mean.
D)
a multiple of the population standard deviation.
(6) You are constructing a 95% confidence interval using the following information: n = 60, = 65.5, s = 2.5, and E = 0.7. What is
the value of the middle of the interval?
A)
0.7
B)
2.5
C)
0.95
D)
65.5
(7) Find the level of confidence assigned to an interval estimate of the mean formed using the interval:
x - 1.96·sx to x + 1.96·s x .
(8) The lengths of 225 fish caught in Lake Michigan had a mean of 15.0 inches. Assume that the population standard deviation is 2.5
inches.
•
Give a point estimate for µ .
•
Find the 90% confidence interval for the population mean length.
(9) In an effort to compare college costs in State of Michigan, a sample of 36 junior students is randomly selected statewide from the
private colleges and 36 more from the public colleges. The private college sample resulted in a mean of $27,650 and the public
college sample mean was $11,360. Assume the annual college fees for private colleges have a mounded distribution and the
standard deviation is $1725. Find the 95% confidence interval for the mean costs for private colleges.
(10) What effect does an increase in the level of confidence have on the width of the confidence interval?
Answers:
(1) True
(2) True
(3) True
(4) True
(5) Option B
(6) Option D
(7) Corresponding to z = 1.96, the confidence level is 95%
(8) (a) Point estimate for the population mean = 15.0 inches
(b) SE = s/sqrt n = 2.5/sqrt 225 = 0.1667
The 90% CI is given by [x-bar - z * SE, x-bar + z * SE]
= [15 - 1.645 * 0.1667, 15 + 1.645 * 0.1667]
= [14.726 inches, 15.274 inches]
(9) SE = s/sqrt n = 1725/sqrt 36 = 287.50
The 95% CI is given by [x-bar - z * SE, x-bar + z * SE]
= [27650 - 1.96 * 287.50, 27650 + 1.96 * 287.50]
= [$27086.50, $28213.50]
(10) The greater the level of confidence, the wider is the confidence interval.