1. Business Research Methods William G. Zikmund
Chapter 21:
Univariate Statistics

2. Univariate Statistics
Test of statistical significance
Hypothesis testing one variable at a time

3. Hypothesis Unproven proposition
Supposition that tentatively explains certain facts or phenomena
Assumption about nature of the world

4. Hypothesis
An unproven proposition or supposition that tentatively explains certain facts or phenomena
Null hypothesis
Alternative hypothesis

5. Null Hypothesis
Statement about the status quo
No difference

6. Alternative Hypothesis
Statement that indicates the opposite of the null hypothesis

7. Significance Level
Critical probability in choosing between the null hypothesis and the alternative hypothesis

8. Significance Level Critical Probability Confidence Level Alpha
Probability Level selected is typically .05 or .01
Too low to warrant support for the null hypothesis

9. The null hypothesis that the mean is equal to 3.0:

10. The alternative hypothesis that the mean does not equal to 3.0:

11. A Sampling Distribution

12. A Sampling Distribution

13. A Sampling Distribution
UPPER
LIMIT
LOWER
LIMIT
m=3.0

14. Critical values of m
Critical value - upper limit

15. Critical values of m

16. Critical values of m
Critical value - lower limit

17. Critical values of m

18. Region of Rejection
LOWER
LIMIT
m=3.0
UPPER
LIMIT

19. Hypothesis Test m =3.0
2.804
m=3.0
3.196
3.78

20. Type I and Type II Errors
Accept null
Reject null
Null is true
Correct-
no error
Type I
error
Null is false
Type II
error
Correct-
no error

21. Type I and Type II Errors
in Hypothesis Testing
State of Null Hypothesis Decision
in the Population Accept Ho Reject Ho
Ho is true Correct--no error Type I error
Ho is false Type II error Correct--no error

22. Calculating Zobs

23. Alternate Way of Testing the Hypothesis

24. Alternate Way of Testing the Hypothesis

25. Choosing the Appropriate Statistical Technique
Type of question to be answered
Number of variables
Univariate
Bivariate
Multivariate
Scale of measurement

26. NONPARAMETRIC
STATISTICS
PARAMETRIC
STATISTICS

27. t-Distribution Symmetrical, bell-shaped distribution
Mean of zero and a unit standard deviation
Shape influenced by degrees of freedom

28. Degrees of Freedom Abbreviated d.f. Number of observations
Number of constraints

29. Confidence Interval Estimate Using the t-distributionor

30. Confidence Interval Estimate Using the t-distribution
= population mean
= sample mean
= critical value of t at a specified confidence
level
= standard error of the mean
= sample standard deviation
= sample size

31. Confidence Interval Estimate Using the t-distribution

34. Hypothesis Test Using the t-Distribution

35. Univariate Hypothesis Test Utilizing the t-Distribution
Suppose that a production manager believes the average number of defective assemblies each day to be 20. The factory records the number of defective assemblies for each of the 25 days it was opened in a given month. The mean was calculated to be 22, and the standard deviation, ,to be 5.

38. Univariate Hypothesis Test Utilizing the t-Distribution
The researcher desired a 95 percent confidence, and the significance level becomes .05.The researcher must then find the upper and lower limits of the confidence interval to determine the region of rejection. Thus, the value of t is needed. For 24 degrees of freedom (n-1, 25-1), the t-value is

41. Univariate Hypothesis Test t-Test

42. Testing a Hypothesis about a Distribution
Chi-Square test
Test for significance in the analysis of frequency distributions
Compare observed frequencies with expected frequencies
“Goodness of Fit”

43. Chi-Square Test

44. Chi-Square Test x² = chi-square statistics
Oi = observed frequency in the ith cell
Ei = expected frequency on the ith cell

45. Chi-Square Test Estimation for Expected Number for Each Cell

46. Chi-Square Test Estimation for Expected Number for Each Cell
Ri = total observed frequency in the ith row
Cj = total observed frequency in the jth column
n = sample size

47. Univariate Hypothesis Test Chi-square Example

48. Univariate Hypothesis Test Chi-square Example

49. Hypothesis Test of a Proportion
p is the population proportion
p is the sample proportion
p is estimated with p

50. Hypothesis Test of a Proportion= H : . 5 p H : . 5 1

53. Hypothesis Test of a Proportion: Another Example
200 , 1 n = 20 . p = n pq S p =
1200 ) 8
)(. 2 (. S p =
1200 16 . S p =
000133 . S p =
0115 . S p =

54. Hypothesis Test of a Proportion: Another Example
200 , 1 n = 20 . p = n pq S p =
1200 ) 8
)(. 2 (. S p =
1200 16 . S p =
000133 . S p =
0115 . S p =

55. Hypothesis Test of a Proportion: Another Example- p Z = S p . 20 - . 15 Z = .
0115 . 05 Z = .
0115 Z = 4 .
348
.001
the
beyond t
significant is it
level.
.05 at
rejected be
should
hypothesis
null so
1.96,
exceeds
value Z
The
Indeed