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De Anza College is interested in the relationship between anxiety level and the need to succeed in school. A random sample of 400 students took a test that measured anxiety level and need to succeed in school. [link] shows the results. De Anza College wants to know if anxiety level and need to succeed in school are independent events.
Need to Succeed in School | High
Anxiety |
Med-high
Anxiety |
Medium
Anxiety |
Med-low
Anxiety |
Low
Anxiety |
Row Total |
---|---|---|---|---|---|---|
High Need | 35 | 42 | 53 | 15 | 10 | 155 |
Medium Need | 18 | 48 | 63 | 33 | 31 | 193 |
Low Need | 4 | 5 | 11 | 15 | 17 | 52 |
Column Total | 57 | 95 | 127 | 63 | 58 | 400 |
a. How many high anxiety level students are expected to have a high need to succeed in school?
a. The column total for a high anxiety level is 57. The row total for high need to succeed in school is 155. The sample size or total surveyed is 400.
$$E=\frac{\text{(row total)(column total)}}{\text{total surveyed}}=\frac{155\cdot 57}{400}=22.09$$
The expected number of students who have a high anxiety level and a high need to succeed in school is about 22.
b. If the two variables are independent, how many students do you expect to have a low need to succeed in school and a med-low level of anxiety?
b. The column total for a med-low anxiety level is 63. The row total for a low need to succeed in school is 52. The sample size or total surveyed is 400.
c. $E=\frac{\text{(row total)(column total)}}{\text{total surveyed}}$ = ________
c. $E=\frac{\text{(row total)(column total)}}{\text{total surveyed}}=8.19$
d. The expected number of students who have a med-low anxiety level and a low need to succeed in school is about ________.
d. 8
DiCamilo, Mark, Mervin Field, “Most Californians See a Direct Linkage between Obesity and Sugary Sodas. Two in Three Voters Support Taxing Sugar-Sweetened Beverages If Proceeds are Tied to Improving School Nutrition and Physical Activity Programs.” The Field Poll, released Feb. 14, 2013. Available online at http://field.com/fieldpollonline/subscribers/Rls2436.pdf (accessed May 24, 2013).
Harris Interactive, “Favorite Flavor of Ice Cream.” Available online at http://www.statisticbrain.com/favorite-flavor-of-ice-cream (accessed May 24, 2013)
“Youngest Online Entrepreneurs List.” Available online at http://www.statisticbrain.com/youngest-online-entrepreneur-list (accessed May 24, 2013).
To assess whether two factors are independent or not, you can apply the test of independence that uses the chi-square distribution. The null hypothesis for this test states that the two factors are independent. The test compares observed values to expected values. The test is right-tailed. Each observation or cell category must have an expected value of at least 5.
Determine the appropriate test to be used in the next three exercises.
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