This is the ANOVA test to answer this question. Be sure to state the null and alternate hypotheses, and briefly answer the question.For students who work, are there differences in the average loan amounts across classes?
Analysis of Variance results:
Where: "Bin(Work)"="0.1 or above"
Responses: Loans
Factors: Class
Response statistics by factor
|
Class
|
n
|
Mean
|
Std. Dev.
|
Std. Error
|
|
1
|
24
|
3434.375
|
1663.0016
|
339.45878
|
|
2
|
21
|
7656.2381
|
1950.798
|
425.69902
|
|
3
|
18
|
10910.833
|
4077.4482
|
961.06375
|
|
4
|
21
|
13134.524
|
6579.8379
|
1435.8383
|
ANOVA table
|
Source
|
DF
|
SS
|
MS
|
F-Stat
|
P-value
|
|
Class
|
3
|
1.1864529e9
|
3.954843e8
|
24.559653
|
<0.0001
|
|
Error
|
80
|
1.2882407e9
|
16103009
|
|
|
|
Total
|
83
|
2.4746936e9
|
|
|
|
Tukey 95% Simultaneous Confidence Intervals:
1 subtracted from
|
Difference
|
Lower
|
Upper
|
P-value
|
|
2
|
4221.8631
|
1075.6672
|
7368.0589
|
0.0039
|
|
3
|
7476.4583
|
4193.408
|
10759.509
|
<0.0001
|
|
4
|
9700.1488
|
6553.953
|
12846.345
|
<0.0001
|
2 subtracted from
|
Difference
|
Lower
|
Upper
|
P-value
|
|
3
|
3254.5952
|
-127.46368
|
6636.6542
|
0.0636
|
|
4
|
5478.2857
|
2228.9086
|
8727.6628
|
0.0002
|
3 subtracted from
|
Difference
|
Lower
|
Upper
|
P-value
|
|
4
|
2223.6905
|
-1158.3684
|
5605.7494
|
0.3176
|
For students that work, is there a relationship between the dollar amount of loans they have and the number of hours per week that they work?
- Compute the coefficient of correlation, the coefficient of determination, and the linear regression equation.
Simple linear regression results:
Dependent Variable: Work
Independent Variable: Loans
Work = 3.5923118 + 0.0010926257 Loans
Sample size: 200
R (correlation coefficient) = 0.51889059
R-sq = 0.26924745
Estimate of error standard deviation: 10.602837
Parameter estimates:
|
Parameter
|
Estimate
|
Std. Err.
|
Alternative
|
DF
|
T-Stat
|
P-value
|
|
Intercept
|
3.5923118
|
0.99406366
|
≠ 0
|
198
|
3.6137644
|
0.0004
|
|
Slope
|
0.0010926257
|
0.00012792287
|
≠ 0
|
198
|
8.5412852
|
<0.0001
|
Analysis of variance table for regression model:
|
Source
|
DF
|
SS
|
MS
|
F-stat
|
P-value
|
|
Model
|
1
|
8201.4492
|
8201.4492
|
72.953552
|
<0.0001
|
|
Error
|
198
|
22259.19
|
112.42015
|
|
|
|
Total
|
199
|
30460.639
|
|
|
|
- Does there appear to be a relationship between work hours and loan amount? Explain your answer.
- Explain the meaning of the coefficient of determination as it applies specifically to this problem.
- Explain the meaning of the slope in the regression equation as it applies specifically to this problem. Is this the relationship you expected? Explain. If it isn't what you expected, explain why it might have occurred.
- Does a linear model appear to be appropriate for this comparison? Explain.
This is the chi-square test of independence. State the null and alternate hypotheses, and explain the results of the test.Is there evidence of a relationship between class and whether or not students work?
Contingency table results:
Rows: Bin(Work)
Columns: Class
|
1
|
2
|
3
|
4
|
Total
|
|
Below 0.1
|
44
|
24
|
28
|
20
|
116
|
|
0.1 or above
|
24
|
21
|
18
|
21
|
84
|
|
Total
|
68
|
45
|
46
|
41
|
200
|
Chi-Square test:
|
Statistic
|
DF
|
Value
|
P-value
|
|
Chi-square
|
3
|
3.2436948
|
0.3556
|