Assignment 8: Statistics and Parameters
Psych 6250
Spring, 2010
Lesson: Statistics and Parameters
1. A measure that arises from your sample is called a ____________
2. A measure that arises from your population is called a _____________
3. The mean, median, mode, variance, and standard deviation of your sample are
_____________
4. The mean, median, mode, variance, and standard deviation of your population
are_______________
5. What symbol represents the mean of the sample?_____
Sample A: Y = 5, 11, 8, 4, 3 (this will be used in many questions below)
6. A researcher samples five scores from a population and obtains the following data.
Compute the mean of Sample A. M=
7. What symbol represents the actual mean of the population?_____
8. Is it possible to compute the actual mean of the population without measuring
everyone in the population? (yes/no)
9. What symbol represents the estimate of the population mean based on the sample?
_______
10. An _________ __________ is one whose expected (mean) value equals the
parameter it is trying to estimate.
11.: Is the sample mean an unbiased estimate of the population mean? (yes/no)
12. Does that mean that the sample mean will always equal the population mean?
(yes/no)
13 Estimate the mean of the population from which Sample A was drawn. est.
μ=_________
14. What can we compute for sure with this sample? (select all that apply)
a: est. μ
b: μ
c: M
15. Which of the following should increase the chances of getting an accurate estimate of
μ out of the sample? (select all that apply)
a:
b:
c:
d:
Draw a larger sample
Draw a smaller sample
Measure something people differ on a lot (i.e. has a large variance)
Measure something people don’t differ on much (i.e. has a small variance)
16. Now we are going to start the process of computing the SS of Sample A using the
computational formula. N=_____
17. ΣY² =______
18. ΣY=______
19. (ΣY)² =
20. SS =
21. What symbol represents the variance of the sample? _____
22. Compute the variance of Sample A (include its symbol in your answer). _________
23. What symbol represents the variance of the population from which the sample was
drawn?_______
24. Would it be possible to compute the actual variance of the population without
measuring everyone in the population? (yes/no)
25. What symbol represents the estimate of the variance of the population from which
the sample was drawn? _______
26 Is the sample variance an unbiased estimate of the population variance? (yes/no)
27. Which of the following is correct?
a: The sample variance is usually greater than the population variance.
b: The sample variance is usually less than the population variance
28. Estimate the variance of the population from which Sample A was drawn.
_________
29. What symbol represents the standard deviation of the sample? ________
30. Compute the standard deviation of Sample A _____
31. What symbol represents the standard deviation of the population from which the
sample was drawn?_____
32. What symbol represents the estimate of the standard deviation of the population
based on the sample?_____
33. Estimate the standard deviation of the population from which Sample A was drawn
._____
34. Of the estimate of the population mean, variance, and standard deviation, which one
is slightly biased?
35. You know that for some sample of 15 scores, that the variance of the sample equals
11. What is the estimate of the population variance? _______
36. You know that for some sample of 9 scores, that the est.σ² =20. What is the variance
of the sample? _______
37. A ____________statistic simply describes the sample.
38. An ___________ statistic uses data from the sample to estimate the parameter of the
population.
39. M, S², S are all....
a: descriptive statistics
b: inferential statistics
c: parameters
40 est. μ, est. σ², est. σ are all....
a: parameters
b: descriptive statistics
c: inferential statistics
41: μ, σ², σ are all....
a: inferential statistics
b: descriptive statistics
c: parameters
42: The 95% ____________ ____________ of the mean is an interval that we are 95%
sure contains the true value of μ.
SPSS
Open up data file ‘Age.sav’, which presents the ages of the CEO’s from a sample of
small companies (defined as those with annual sales greater than $5 million and less than
$350 million). Source: Forbes, November 8, 1993 as provided in
http://lib.stat.cmu.edu/DASL/DataArchive.html.
In SPSS go to Analyze>>Descriptive Statistics>>Explore. Put the variable into the
dependent list, click on ‘Plots’, under ‘BoxPlots’ select none, under ‘Descriptive’ select
‘Histogram’ and then view the output.
Note that when SPSS reports the ‘variance’ it is giving the estimate of the population
variance, and when it reports ‘std. deviation’ it is giving the estimate of the population
standard deviation. Two of the values I will be asking for below are not directly provided
by SPSS. For one of them you may need to pull out a formula from the lecture. For the
other, ‘SS’, I’ll tell you how to do it. As SPSS gives you the est.σ², and we know that
est.σ² = (SS)/(N-1), it is a simple matter to figure out that SS = (est.σ²)(N-1)
First, look at the histogram to see what the distribution of ages for the CEO’s looks like.
I won’t be asking a question about this but looking at a histogram of the data is almost
always my first step in understanding the sample.
43. est. μ = _______
44 & 45. The 95% confidence interval for the mean is _______ ≤ μ ≤ ________
46. est.σ² =_______
47. est.σ =_______
48. SS=_______
49. S²=_______