1.
mean = 25 and standard deviation = 7.0711
3.
when the number of degrees of freedom is greater than 90
5.
\(df = 2\)
6.
a test of a single variance
8.
a left-tailed test
10.
\(H_0: \sigma^2 = 0.812\);
\(H_a: \sigma^2 > 0.812\).
12.
a test of a single variance
16.
a goodness-of-fit test
18.
3
20.
2.04
21.
We decline to reject the null hypothesis. There is not enough evidence to suggest that the observed test scores are significantly different from the expected test scores.
23.
\(H_0\): the distribution of AIDS cases follows the ethnicities of the general population of Santa Clara County.
25.
right-tailed
27.
2016.136
28.
- 30.
a test of independence
a test of independence
34.
8
36.
6.6
39.
| Smoking level per day | African American | Native Hawaiian | Latino | Japanese Americans | White | Totals |
|---|
| 1-10 | 9,886 | 2,745 | 12,831 | 8,378 | 7,650 | 41,490 |
| 11-20 | 6,514 | 3,062 | 4,932 | 10,680 | 9,877 | 35,065 |
| 21-30 | 1,671 | 1,419 | 1,406 | 4,715 | 6,062 | 15,273 |
| 31+ | 759 | 788 | 800 | 2,305 | 3,970 | 8,622 |
| Totals | 18,830 | 8,014 | 19,969 | 26,078 | 27,559 | 10,0450 |
Table \(\PageIndex{54}\)
41.
| Smoking level per day | African American | Native Hawaiian | Latino | Japanese Americans | White |
|---|
| 1-10 | 7777.57 | 3310.11 | 8248.02 | 10771.29 | 11383.01 |
| 11-20 | 6573.16 | 2797.52 | 6970.76 | 9103.29 | 9620.27 |
| 21-30 | 2863.02 | 1218.49 | 3036.20 | 3965.05 | 4190.23 |
| 31+ | 1616.25 | 687.87 | 1714.01 | 2238.37 | 2365.49 |
Table \(\PageIndex{55}\)
43.
10,301.8
44.
right
46.
- 48.
test for homogeneity
test for homogeneity
52.
All values in the table must be greater than or equal to five.
54.
3
57.
a goodness-of-fit test
59.
a test for independence
61.
Answers will vary. Sample answer: Tests of independence and tests for homogeneity both calculate the test statistic the same way \(\sum_{(i j)} \frac{(O-E)^{2}}{E}\). In addition, all values must be greater than or equal to five.
63.
true
65.
false
67.
225
69.
\(H_0: \sigma^2 \leq 150\)
71.
36
72.
Check student’s solution.
74.
The claim is that the variance is no more than 150 minutes.
76.
a Student's \(t\)- or normal distribution
78.
- 80.
- 82.
- 84.
- 87.
| Marital status | Percent | Expected frequency |
|---|
| Never married | 31.3 | 125.2 |
| Married | 56.1 | 224.4 |
| Widowed | 2.5 | 10 |
| Divorced/Separated | 10.1 | 40.4 |
Table \(\PageIndex{56}\)
- 89.
- 91.
- 94.
true
false
98.
- 100.
- 102.
- 104.
- 106.
- 108.
true
true
112.
- 114.
- 116.
- 118.
- 120.
- 122.
- The test statistic is always positive and if the expected and observed values are not close together, the test statistic is large and the null hypothesis will be rejected.
- Testing to see if the data fits the distribution “too well” or is too perfect.
