c Chi-squared test of a contingency table
:H0
The two variables (County and party in 2004) are independent
:H1
The two variables are dependent
=
−
=
6
1i i
2
ii
2
e
)ef(
1
2
3
A B C D
Contingency Table
Broward Miami-Dade TOTAL
A16.15 t-test of ρ
0:H0=
0:H1
1
2
3
A B
© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
1
2
A B C D
t-Estimate: Mean
Case A16.1 Relationship between interest rates and sales: t-test of ρ or β1
:H
0
= 0
:H1
0
1
2
3
A B
Correlation
Rates and Sales
Relationship between interest rates and ages: Spearman rank correlation coefficient test
:H
0
= 0
:H1
0
Rates and Age
1
2
A B
Correlation
Difference between sales: Unequal variances t– test of µ1– µ2
0
H
: µ1– µ2 = 0
.
:H1
µ1– µ2 < 0
1
2
3
4
5
A B C
t-Test: Two-Sample Assuming Unequal Variances
W Sales M Sales
Mean 552 1183
Variance 60133 128618
Difference between ages: Unequal variances t- test of µ1– µ2
0
H
: µ1– µ2 = 0
.
:H1
µ1– µ2 < 0
1
2
3
4
5
A B C
t-Test: Two-Sample Assuming Unequal Variances
W Age M Age
Mean 9.24 12.58
Variance 15.98 27.05
Interest rates among the 3 types of businesses: One-way analysis of variance
:H0
µ1= µ2 = µ3
:H1
At least two means differ
10
15
A B C D E F G
ANOVA
Gender of type of business: Ch-squared test of a contingency table
:H0
The two variables (gender of business) are independent
:H1
The two variables are dependent
1
2
3
4
A B C D E F
Contingency Table
Gender
Business 1 2 3 TOTAL
Case A16.2a t-tests of
D
Weight
1
2
3
4
A B C
t-Test: Paired Two Sample for Means
Weight 1 Weight 2
Mean 79.89 78.62
Cholesterol
1
2
3
A B C
t-Test: Paired Two Sample for Means
Choles 1 Choles 2
Fat intake
1
2
3
4
A B C
t-Test: Paired Two Sample for Means
TotFat 1 TotFat 2
Mean 66.56 46.72
Cholesterol intake
1
2
3
4
A B C
t-Test: Paired Two Sample for Means
DietC 1 DietC 2
Mean 242.42 177.12
Calories from fat
1
2
3
4
5
A B C
t-Test: Paired Two Sample for Means
PDCF 1 PDCF 2
Mean 36.54 30.82
Variance 56.72 49.71
b Equal-variances t-test of
21 −
Weight reduction
1
2
6
Observations 16 17
3
4
5
A B C
t-Test: Two-Sample Assuming Equal Variances
Female Male
Mean 1.32 1.22
Variance 1.54 11.17
Cholesterol reduction
1
2
3
4
5
6
A B C
t-Test: Two-Sample Assuming Equal Variances
Female Male
Mean 0.48 0.72
Variance 0.48 0.55
Observations 16 17
Fat intake reduction
1
2
3
4
5
6
A B C
t-Test: Two-Sample Assuming Equal Variances
Female Male
Mean 14.50 24.88
Variance 229.91 906.76
Observations 16 17
Cholesterol intake reduction
1
2
3
4
5
6
A B C
t-Test: Two-Sample Assuming Equal Variances
Female Male
Mean 38.46 90.56
Variance 5683 46984
Observations 16 17
Calories from fat reduction
1
2
3
4
5
A B C
t-Test: Two-Sample Assuming Equal Variances
Female Male
Mean 6.88 4.62
Variance 18.69 34.29
c t-test of
or
1
0:H0=
or
0:H 10 =
Age and weight reduction
1
2
A B C D
Correlation
Age and cholesterol reduction
© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
1
2
A B C D
Correlation
Age and Fat intake reduction
1
2
3
A B C D
Correlation
Age and TotFat
Age and Cholesterol intake reduction
1
2
3
4
A B C D
Correlation
Age and Dietc
Pearson Coefficient of Correlation
-0.1258
Age and Calories from fat reduction
1
2
3
A B C D
Correlation
Age and PDCF