Download Exam III Fall 2000

BUSA 3321 Exam 3 – Fall 2000
1. Let X be a binomial random variable with n=20 and p=.30. Use the binomial table
to find P [X=2].
a. .027
b. .004
c. .023
d. none of the above
2. Let X be a binomial random variable with n=20 and p=.30. The expected value
(mean) of X is
a. 4
b. 5
c. 6
d. none of the above
3. Let X be a binomial random variable with n=20 and p=.30. The variance of X is
a. 2.5
b. 3.5
c. 4.2
d. none of the above
4. Which of the following is not necessary for a binomial random variable X
a. N trials
b. Probability p of success on each trial
c. Independence from trial to trial
d. Mutually exclusive outcomes from one trial to the next trial
5. Suppose a jury panel of several thousand persons has 17% African-Americans.
What is the probability that a jury of 6 persons will have no African-Americans?
Choose the answer correct to two decimal places.
a. .67
b. .33
c. .83
d. none of the above
6. Suppose a jury panel of several thousand persons has 50% women. What is the
probability that a jury of 6 persons will have exactly 5 women and 1 man?
Choose the answer correct to two decimal places
a. .10
b. .90
c. .02
d. none of the above
7. Which of the following have perfectly normal distributions
a. The sample mean for a normal random variable with samples of size 20
b. The binomial distribution for a sufficiently large number of trials
c. The sample proportion for sufficiently large samples
d. All of the above
8. Given that the random variable X is normally distributed with a mean of 80 and a
standard deviation of 10, P[85<X<90] is
a. .5328
b. .3413
c. .1915
d. .1498
9. If the z-value for a given value x of the random variable X is z=1.96, and the
distribution of X is normal with a mean of 60 and a standard deviation of 6, to
what x-value does this z-value correspond?
a. 71.76
b. 67.96
c. 61.96
d. none of the above
10. Researchers studying the effects of a new diet found that the weight loss over a
one-month period by those on the diet was normally distributed with a mean of 9
pounds and a standard deviation of 3 pounds. What proportion of dieters loses
more than 12 pounds?
a. .3413
b. .1587
c. .8413
d. none of the above
11. What proportion of the dieters gained weight?
a. .4987
b. .0013
c. .5
d. none of the above
12. If all possible samples of size 36 are drawn from a non-normal population, the
probability distribution of the sample mean is best described as
a. Non-normal
b. Perfectly normal
c. Approximately normal
d. None of the above
13. X is a random variable with a standard deviation of 72. Samples of size 36 are
drawn. The standard error of the sampling distribution of the sample mean is
a. 72
b. 72^2
c. 2
d. none of the above
14. The expected value (mean) of the sample mean is
a. The population mean, i.e. the mean of the random variable X
b. Unknown
c. Proportional to the square root of n
d. All of the above
15. A population has a mean of 60 and a standard deviation of 8. A sample of 50
observations will be taken at random from the population. The probability that the
sample mean will be between 57 and 62 is
a. .9576
b. .9960
c. .2467
d. .3520
16. A sample of 100 observations will be selected at random from a large population
with a population proportion of .5. The standard error of the sampling distribution
of the sample proportion is
a. .025
b. .05
c. .5
d. none of the above
17. For the sample proportion defined above, the expected value (mean) is
a. .025
b. .05
c. .5
d. none of the above
18. The exact distribution of the sample proportion is binomial. However, for
sufficiently large samples, the distribution of the sample proportion is
approximately normal. Sufficiently large means
a. n>30
b. np>5 and n(1-p)>5
c. both of the above, i.e. a and b
d. none of the above
19. A 98% confidence interval estimate for a population mean is determined to be
75.38 to 86.52. If the confidence level is reduced to 90%, the confidence interval
for 
a. Becomes wider
b. Remains the same
c. Becomes narrower
d. None of the above
20. A financial analyst wanted to determine the mean annual return on all mutual
funds. A random sample of 60 returns shows a mean of 12%. If the population
standard deviation is assumed to be 4%, estimate with 95% confidence the mean
annual return on all funds.
a. 10.99% to 13.01%
b. 11.15% to 12.84%
c. 4% to 20%
d. none of the above
21. A statistician wants to estimate the mean weekly expenditure on clothes to within
$5 with a 90% confidence interval. From historical data, the standard deviation of
the weekly expenditure on clothes is $125. How large a sample must be taken?
a. 9
b. 97
c. 68
d. none of the above
22. The width of a confidence interval estimate of the population proportion (like the
number of voters for Bush) widens when the
a. Level of confidence increases
b. Sample size decreases
c. Sample proportion is nearer .5
d. All of the above
Hint: try computing the width of a 95% confidence interval from a sample of
100 voters first when the sample proportion is .3; then when it is .5
23. Which of the following statements is false
a. The null hypothesis gets the benefit of the doubt.
b. The data can only support the alternative hypothesis.
c. The decision to be made in hypothesis testing is whether or not the
evidence against the null hypothesis rises to a pre-set standard known as
alpha, the significance level
d. All of the above statements are true
24. Suppose the null hypothesis is H0: p< .5 and the alternative is H1: p >.5. The
Decision rule is “Reject H0 if standardized p-hat, the sample proportion, > 1.96.
Then the significance level, of the test must be
a. .05
b. .025
c. .10
d. not enough information to tell
25. For the above problem, suppose the observed value of the test statistic is 2.5.
The decision would be
a. Reject H0
b. Fail to reject H0
c. Reject H1
d. None of the above