True/False
Indicate whether the sentence or statement is true
or false.


1.

For
any distribution, a zscore of z = 0.50 corresponds to a location below the mean.


2.

On an
exam, Tom scored 8 points above the mean and had a zscore of +2.00. The standard deviation for the
set of exam scores must be s = 4.


3.

In
any population of scores, at least one individual will have a zscore of zero.


4.

The
value for a probability can never exceed 1.00, unless you have made a computational
error.


5.

If
there are 50 students in a class, then the probability of randomly selecting any particular
individual is p = 1/50.


6.

When
the zscore value in a normal distribution is negative, the body of the distribution is on the
righthand side.


7.

Whenever the statistical decision is to reject the null hypothesis, there is a risk of
a Type I error.


8.

If a
specific sample leads to rejecting the null hypothesis with a = .01, then the same sample would also lead to rejecting the null
hypothesis with a = .05.


9.

There
is always a possibility that the decision reached in a hypothesis test is incorrect.


10.

Assuming that all other factors are held constant, as the population variability
increases, the standard error also increases.


11.

A
population has m = 50 and
s = 10. For a
sample of n = 4 scores from this population, a sample mean of X (overbar) = 55 would be considered
an extreme value.


12.

A
sample of n = 4 scores is randomly selected from a population with m = 80 and
s = 16. If the
sample mean is X (overbar) = 84, then the corresponding zscore is z = +1.00.


13.

In a
t statistic, the estimated standard error provides a measure of how much difference is reasonable to
expect between a sample mean and the population mean.


14.

As
sample size increases, the estimated standard error tends to decrease.


15.

Assuming all other factors are held constant, t statistics tend to be more variable
than zscores.

Multiple Choice
Identify the
letter of the choice that best completes the statement or answers the question.


16.

A
population of scores has s = 20. In this population, a score of X = 80 corresponds to z = +0.25. What is the
population mean?


17.

A
zscore of z = 0.25 indicates a location that is ______. a.  at the center of
the distribution  b.  slightly below the mean  c.  far below the
mean in the extreme lefthand tail of the distribution  d.  The location
depends on the mean and standard deviation for the distribution.   


18.

A
population with m = 85 and s = 12 is transformed into zscores. After the transformation, the population of
zscores will have a mean of _____. a.  m = 85  b.  m = 1.00  c.  m = 0  d.  cannot be determined from the information
given   


19.

A jar
contains 40 red marbles and 10 black marbles. If you take a random sample of n = 3 marbles
from this jar, and the first two marbles are both red, what is the probability that the third marble
will be black? a.  10/50  b.  8/48  c.  9/48  d.  10/48   


20.

What
proportion of the scores in a normal distribution have zscores less than z = 0.86? a.  0.3051  b.  0.1949  c.  0.8051  d.  0.6949   


21.

For a
normal distribution, what zscore value separates the highest 10% of the distribution from the lowest
90%? a.  z =
0.90  b.  z =
0.90  c.  z = 1.28  d.  z =
1.28   


22.

By
definition, a Type I error is ______. a.  rejecting a false
H_{1}  b.  rejecting a false
H_{0}  c.  rejecting a true H_{0}  d.  failing to
reject a false H_{0}   


23.

A
researcher expects a treatment to produce an increase in the population mean. Assuming a normal
distribution, what is the critical zscore for a onetailed test with a =
.01? a.  +2.33  b.  ±2.58  c.  +1.65  d.  ±2.33   


24.

The
probability of a Type II error is expressed as ______.


25.

In
general, the standard error of X (overbar) gets smaller as ______. a.  sample size and
standard deviation both increase  b.  sample size and standard deviation both
decrease  c.  sample size increases and standard deviation
decreases  d.  sample size decreases and standard deviation
increases   


26.

A
random sample of n = 4 scores is obtained from a population with s = 10. If the
sample mean is 10 points greater than the population mean, then the sample mean would have a zscore
of ______. a.  +10.00  b.  +2.00  c.  +1.00  d.  cannot be determined without knowing the population
mean   


27.

If a
sample is selected from a normal population, then the probability that the sample mean will have a
zscore greater than z = 2.00 is ______. a.  p = 0.0228  b.  p =
0.9772  c.  p = 0 .0456  d.  cannot determine
without knowing the sample size   


28.

The
major difference between the t statistic formula and the zscore formula is ______. a.  the t statistic
uses the sample variance in place of the population variance  b.  the t statistic
uses the sample mean in place of the population mean  c.  the t statistic
computes standard error by dividing the standard deviation by df = n  1 instead of dividing by
n  d.  all of the
above   


29.

The
magnitude of the estimated standard error is ______. a.  directly related
to sample variance and directly related to sample size  b.  directly related
to sample variance and inversely related to sample size  c.  inversely
related to sample variance and directly related to sample size  d.  inversely
related to sample variance and inversely related to sample size   


30.

A
sample of n = 25 scores produces a t statistic of t = 2.05. If the researcher is using a twotailed
test with a = .05, the
correct statistical decision is ______. a.  reject the null hypothesis  b.  fail to reject
the null hypothesis  c.  cannot answer without additional
information   

Other


31.

For a
population with m = 50 and s = 4, find the X value that corresponds to each of the following
zscores.
z = 1.50  X =
______  z =
+0.25  X = ______  z = +2.00  X = ______  z = 1.25  X =
______   


32.

A
normal distribution has a mean of m = 61 with s = 8. Find the following probabilities:
a.  p(X > 66)  b.  p(X < 55)  c.  p(X < 70)  d.  p(51 < X < 73)   


33.

The
term error is used in two different ways in hypothesis testing:
a.  Type I error (or Type II)  b.  standard error   
What can a researcher do to influence the size of the
standard error? Does this action have any effect on the probability of a Type I error? What can a
researcher do to influence the probability of a Type I error? Does this action have any effect on the
size of the standard error?


34.

A
normal distribution has m = 40 and s = 8.
a.  Describe the distribution of sample means based on samples of n
= 16 selected from this population.  b.  Of all the possible samples of n = 16, what proportion will
have sample means greater than 42?  c.  Of all the possible samples of n = 16, what proportion will
have sample means less than 39?   


35.

A
sample of freshmen takes a reading comprehension test and their scores are summarized below. If the
mean for the general population on this test is m = 12, can you conclude that this sample is significantly different
from the population. Test with a = .05.
Sample Scores: 16, 8, 8, 6, 9, 11, 13, 9, 10
