Statistics- When a distribution has more values to the right and tails

True/False: (Each question is worth 2 points)

Indicate
whether the statement is true or false.

____ 1. When a distribution has more values to the
right and tails to the left, we say it is skewed negatively.

____ 2. Assume that A and B are
independent events with P(A) = 0.30 and P(B) =
0.50. The probability that both events will occur simultaneously is 0.80.

____ 3. Two measurements from the same individuals is
an example of data collected from a matched pairs experiment.

____ 4. The probability that a standard normal random
variable Z is less than-3.5 is approximately
0.

____ 5. If the value of the Durbin-Watson test
statistic, d, satisfies the inequalities d < d_L
or d > 4- d_L,
where d_L and d_U are the critical values of d,
we conclude that positive first-order autocorrelation exists.

____ 6. In market segmentation, if education is the
segmentation variable of interest, then possible segments of the market
include: some high school, high school graduates, some college, college or
university graduates.

____ 7. A simple linear regression equation is given
by . The point estimate of y when x
= 4 is 20.45.

____ 8. A cumulative relative frequency distribution
lists the number of observations that lie below each of the class limits.

____ 9. If P(A) = 0.4 and P(B)
= 0.6, then A and B must be collectively exhaustive.

____ 10. Recall the rule of thumb used to indicate
when the normal distribution is a good approximation of the sampling
distribution for the sample proportion . For the combination n = 50, p
= 0.05, the rule is satisfied.

Multiple
Choice: (Each question is worth 5
points)

Identify
the choice that best completes the statement or answers the question.

____ 11. The average score for a class of 30 students
was 75. The 15 male students in the class averaged 70. The 15 female students
in the class averaged:

a.	85.
b.	80
c.	75
d.	70

____ 12. Which of the following must be avoided in
designing a survey?

a.	Dichotomous questions.
b.	Leading questions.
c.	Demographic questions.
d.	All of these choices are true.

____ 13. If X and Y are random
variables, the sum of all the conditional probabilities of X given a
specific value of Ywill always be:

a.	0.0
b.	1.0
c.	the average of the possible values of X.
d.	the average of the possible values of Y.

____ 14. Which of the following is equivalent to P(A|B)?

a.	P(A and B)
b.	P(B|A)
c.	P(A)/P(B)
d.	None of these choices.

____ 15. The owner of a meat market has an assistant
who has determined that the weights of roasts are normally distributed, with a
mean of 3.2 pounds and standard deviation of 0.8 pounds. If a sample of 25
roasts yields a mean of 3.6 pounds, what is the Z-score for this sample
mean?

a.	-2.50
b.	2.50
c.	-0.50
d.	None of these choices.

____ 16. If A and B are independent
events with P(A) = 0.60 and P(B) = 0.70, then P(A
or B) equals:

a.	1.30
b.	0.88
c.	0.42
d.	Cannot tell from the given information.

____ 17. For which type of data are the values
arbitrary numbers?

a.	Interval data
b.	Nominal data
c.	Ordinal data
d.	None of these choices.

____ 18. Which of the following cannot have a Poisson
distribution?

a.	The length of a movie.
b.	The number of telephone calls received by a switchboard in a specified time period.
c.	The number of customers arriving at a gas station in Christmas day.
d.	The number of bacteria found in a cubic yard of soil.

____ 19. A and B are disjoint events,
with P(A) = 0.20 and P(B) = 0.30. Then P(A
and B) is:

a.	0.50
b.	0.10
c.	0.00
d.	0.06

____ 20. The width of the confidence interval estimate
for the predicted value of y depends on

a.	the standard error of the estimate
b.	the value of x for which the prediction is being made
c.	the sample size
d.	All of these choices are true.

____ 21. An approach of assigning probabilities which
assumes that all outcomes of the experiment are equally likely is referred to
as the:

a.	subjective approach
b.	objective approach
c.	classical approach
d.	relative frequency approach

____ 22. The owner of a local nightclub has recently
surveyed a random sample of n = 300 customers of the club. She would now
like to determine whether or not the mean age of her customers is over 35. If
so, she plans to alter the entertainment to appeal to an older crowd. If not,
no entertainment changes will be made. Suppose she found that the sample mean
was 35.5 years and the population standard deviation was 5 years. What is the p-value
associated with the test statistic?

a.	0.9582
b.	1.7300
c.	0.0418
d.	0.0836

____ 23. If an experiment consists of five outcomes
with P(O₁) = 0.10, P(O₂) =
0.20, P(O₃) = 0.30, P(O₄) =
0.25, then P(O₅) is

a.	0.75
b.	0.15
c.	0.50
d.	Cannot be determined from the information given.

____ 24. The Sutton police department must write, on
average, 6 tickets a day to keep department revenues at budgeted levels.
Suppose the number of tickets written per day follows a Poisson distribution
with a mean of 6.5 tickets per day. Interpret the value of the mean.

a.	The mean has no interpretation.
b.	The expected number of tickets written would be 6.5 per day.
c.	Half of the days have less than 6.5 tickets written and half of the days have more than 6.5 tickets written.
d.	The number of tickets that is written most often is 6.5 tickets per day.

____ 25. After calculating the sample size needed to
estimate a population proportion to within 0.04, your statistics professor told
you the maximum allowable error must be reduced to just .01. If the original
calculation led to a sample size of 800, the sample size will now have to be:

a.	800
b.	3,200
c.	6,400
d.	12,800

____ 26. Which of the following tests is appropriate
for nominal data if the problem objective is to compare two or more populations
and the number of categories is at least 2?

a.	The z-test for one proportion, p, or difference of two proportions, p1 – p2.
b.	The chi-squared goodness-of-fitness test.
c.	The chi-squared test of a contingency table.
d.	All of these choices are true.

____ 27. In constructing a confidence interval
estimate for the difference between two population proportions, we:

a.	pool the population proportions when the populations are normally distributed.
b.	pool the population proportions when the population means are equal.
c.	pool the population proportions when they are equal.
d.	never pool the population proportions.

____ 28. Given that Z is a standard normal
variable, the variance of Z:

a.	is always greater than 2.0.
b.	is always greater than 1.0.
c.	is always equal to 1.0.
d.	cannot assume a specific value.

____ 29. The sampling distribution of the test statistic
for a goodness-of-fit test with k categories is a:

a.	chi-squared distribution with k– 1 degrees of freedom.
b.	normal distribution.
c.	Student t-distribution with k– 1 degrees of freedom.
d.	None of these choices.

____ 30. The least squares method minimizes which of
the following sum of squares?

a.
b.
c.
d.	All of these choices are true

____ 31. In testing for the differences between the
means of two independent populations where the variances in each population are
unknown but assumed equal, the degrees of freedom is:

a.	n1 + n2
b.	n1 + n2 – 2
c.	n1 + n2 – 1
d.	None of these choices

____ 32. For testing the difference between two
population proportions, the pooled proportion estimate is found by taking:

a.	the proportion of successes from sample 1 plus the proportion of successes from sample 2.
b.	the total number of successes in both samples divided by the total of both sample sizes.
c.	the difference between the proportion of successes in each sample.
d.	None of these choices.

____ 33. The hypothesis of most interest to the researcher
is:

a.	the alternative hypothesis.
b.	the null hypothesis.
c.	both hypotheses are of equal interest.
d.	Neither hypothesis is of interest.