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Determine the appropriate test to be used in the next three exercises.
A pharmaceutical company is interested in the relationship between age and presentation of symptoms for a common viral infection. A random sample is taken of 500 people with the infection across different age groups.
a test of independence
The owner of a baseball team is interested in the relationship between player salaries and team winning percentage. He takes a random sample of 100 players from different organizations.
A marathon runner is interested in the relationship between the brand of shoes runners wear and their run times. She takes a random sample of 50 runners and records their run times as well as the brand of shoes they were wearing.
a test of independence
Use the following information to answer the next seven exercises: Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of 200 passengers is taken.
[link] shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel.
| Traveling Distance | Third class | Second class | First class | Total |
|---|---|---|---|---|
| 1–100 miles | 21 | 14 | 6 | 41 |
| 101–200 miles | 18 | 16 | 8 | 42 |
| 201–300 miles | 16 | 17 | 15 | 48 |
| 301–400 miles | 12 | 14 | 21 | 47 |
| 401–500 miles | 6 | 6 | 10 | 22 |
| Total | 73 | 67 | 60 | 200 |
State the hypotheses.
H
0 : _______
H
a : _______
How many passengers are expected to travel between 201 and 300 miles and purchase second-class tickets?
How many passengers are expected to travel between 401 and 500 miles and purchase first-class tickets?
6.6
What is the test statistic?
What can you conclude at the 5% level of significance?
Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans and 7,650 whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites.
Complete the table.
| Smoking Level Per Day | African American | Native Hawaiian | Latino | Japanese Americans | White | TOTALS |
|---|---|---|---|---|---|---|
| 1-10 | ||||||
| 11-20 | ||||||
| 21-30 | ||||||
| 31+ | ||||||
| TOTALS |
| 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 |
State the hypotheses.
H
0 : _______
H
a : _______
Enter expected values in [link] . Round to two decimal places.
Calculate the following values:
| 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 |
df = _______
p -value = ______
Is this a right-tailed, left-tailed, or two-tailed test? Explain why.
right
Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade in the region corresponding to the p -value.
State the decision and conclusion (in a complete sentence) for the following preconceived levels of α .
α = 0.05
α = 0.01
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