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Suppose that 600 thirty–year–olds were surveyed to determine whether or not there is a relationship between the level of education an individual has and salary. Conduct a test for independence.
| Annual Salary | Not a high school graduate | High school graduate | College graduate | Masters or doctorate |
|---|---|---|---|---|
| <$30,000 | 15 | 25 | 10 | 5 |
| $30,000 - $40,000 | 20 | 40 | 70 | 30 |
| $40,000 - $50,000 | 10 | 20 | 40 | 55 |
| $50,000 - $60,000 | 5 | 10 | 20 | 60 |
| $60,000 + | 0 | 5 | 10 | 150 |
A Psychologist is interested in testing whether there is a relationship between personality types and majors majors. The results of the study are shown below. Conduct a Test of Independnce. Test at a 5% level of significance.
| Open | Conscientious | Extrovert | Agreeable | Neurotic | |
| Business | 41 | 52 | 46 | 61 | 58 |
| Social Science | 72 | 75 | 63 | 80 | 65 |
Do men and women select different breakfasts? The breakfast ordered by randomly selected men and women at a popular breakfast place is shown below. Conduct a test of independance. Test at a 5% level of significance
| French Toast | Pancakes | Waffles | Omelettes | |
| Men | 47 | 35 | 28 | 53 |
| Women | 65 | 59 | 55 | 60 |
Is there a relationship between the distribution of community college statistics students and the distribution of university statistics students in what technology they use on their homework? Of the randomly selected community college students 43 used a computer, 102 used a calculator with built in statistics functions, and 65 used a table from the textbook. Of the randomly selected university students 28 used a computer, 33 used a calculator with built in statistics functions, and 40 used a table from the textbook. Conduct an appropriate hypothesis test using a 0.05 level of significance.
A fisherman is interested in whether the distribution of fish caught is independent of the fishing lake. Of the 191 randomly selected fish caught in Green Valley Lake, 105 were rainbow trout, 27 were other trout, 35 were bass, and 24 were catfish. Of the 293 randomly selected fish caught in Echo Lake, 115 were rainbow trout, 58 were other trout, 67 were bass, and 53 were catfish. Perform the hypothesis test at a 5% level of significance.
As the degrees of freedom increase, the graph of the chi-square distribution looks more and more symmetrical.
True
The standard deviation of the chi-square distribution is twice the mean.
False
The mean and the median of the chi-square distribution are the same if .
False
In general, if the observed values and expected values of a Test for Independance are not close together, then the test statistic can get very large and on a graph will be way out in the right tail.
True
The degrees of freedom for a Test for Independence are equal to the sample size minus 1.
False
The Test for Independence uses tables of observed and expected data values.
True
The test to use when determining if the college or university a student chooses to attend is related to his/her socioeconomic status is a Test for Independence.
True
In a Test of Independence, the expected number is equal to the row total multiplied by the column total divided by the total surveyed.
True
In a Test for Independance, if the p-value is 0.0113, in general, do not reject the null hypothesis.
False
For a Chi-Square distribution with degrees of freedom of 17, the probability that a value is greater than 20 is 0.7258.
False
If , the chi-square distribution has a shape that reminds us of the exponential.
True
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