Name: 
 

PSY295 Spring 2003 Exam II Review



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

1. 

For any distribution, a z-score 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 z-score 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 z-score 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 z-score value in a normal distribution is negative, the body of the distribution is on the right-hand 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 (over-bar) = 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 (over-bar) = 84, then the corresponding z-score 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 z-scores.
 

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?
a.
70
b.
75
c.
85
d.
90
 

17. 

A z-score 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 left-hand 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 z-scores. After the transformation, the population of z-scores 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 z-scores less than z = 0.86?
a.
0.3051
b.
0.1949
c.
0.8051
d.
0.6949
 

21. 

For a normal distribution, what z-score 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 H1
b.
rejecting a false H0
c.
rejecting a true H0
d.
failing to reject a false H0
 

23. 

A researcher expects a treatment to produce an increase in the population mean. Assuming a normal distribution, what is the critical z-score for a one-tailed 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 ______.
a.
b
b.
1 - b
c.
a
d.
1 - a
 

25. 

In general, the standard error of X (over-bar) 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 z-score 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 z-score 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 z-score 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 two-tailed 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 z-scores.

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
 



 
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