1. How many degrees of freedom does the sample variance have when calculated from a sample of n observations? a. n b. n - 1 c. n + 1 d. none of the above 2. If X, Y, and Z are random variables and a and b are constants, then the expected value of Z = aX +bY is a. aE(X) - bE(Y) b. aE(X) + bE(Y) c. E(X) - E(Y) d. E(X) - E(Y) 3. The covariance between two random variables X and Y is a. E[(X - X)(Y- Y)] b. E(XY)2 - XY c. E(XY)2 - (XY)2 d. none of the above 4. If X is a normal random variable that has mean = 20 and standard deviation = 2, the standardized value of X = 16 is a. 4 b. -2 c. 2 d. -4 Solution 1. b 2. b 3. a 4. b (16-20)/2 = -2.

1. 1. How many degrees of freedom will thetdistribution have when constructing an interval
estimate for the difference between the means of two populations if the two population standard
deviations are unknown and assumed unequal and the samples sizes of groups 1 and 2 aren1= 11
andn2= 15?
2. A physical education teacher is interested in whether, on average, third grade students are
taller this year as compared to last year. Independent random samples of students from this year
and last year were taken and their heights (in inches) were noted. You are given the following
results.
What is the 90% confidence interval for the difference between the two population mean
heights?
What is the test statistic used in the hypothesis test for the difference between the two
populations means?
If the null hypothesis tested isH0:?d= 0, what is the test statistic for the difference between the
two population means?
5. When each data value in one sample is paired with a corresponding data value in another
sample for a sample of 35 individuals or objects and the corresponding difference are computed,
what type of distribution will the difference data have? a.26 degrees of freedom b.24 degrees of
freedom c.11 degrees of freedom
d.Not enough information is given to compute the degrees of freedom.
2. A physical education teacher is interested in whether, on average, third grade students are

2. taller this year as compared to last year. Independent random samples of students from this year
and last year were taken and their heights (in inches) were noted. You are given the following
results.
What is the 90% confidence interval for the difference between the two population mean
heights? a..033 to 3.767 b..824 to 2.976 c.?.349 to 4.149 d..604 to 3.196
3. The following information was obtained from independent random samples. Suppose we are
interested in testingH0:?1??2= 50 andHa:?1??2? 50
What is the test statistic used in the hypothesis test for the difference between the two
populations means? a.15.88 b.?3.19 c..002 d.?1.51
4. The following information was obtained frommatched samples.
If the null hypothesis tested isH0:?d= 0, what is the test statistic for the difference between the
two population means? a.?3.20 b.?1.44 c..223 d.48.68

3. 5. When each data value in one sample is paired with a corresponding data value in another
sample for a sample of 35 individuals or objects and the corresponding difference are
computed, what type of distribution will the difference data have? a.matched pairs distribution
b.exponential distribution c.uniform distribution d.tdistribution
Solution
b. 24 degrees of freedom b. .824 to 2.976 c. .002 c. .223 . exponential distribution