Question

7. Choose the appropriate statistical measure for each proposed study.

A researcher and sports enthusiast is interested in knowing if the salaries of professional baseball players are significantly higher or lower than the salaries of professional basketball players. She samples 100 professional baseball players and 100 professional basketball players in order to compare their salaries. Which statistical procedure would you apply to determine whether there was a significant difference between baseball and basketball players in terms of their salaries?

A teacher is interested in the relationship between her students' attendance and their performance on a statewide standardized test. She believes that the fewer days of school a student misses the better they will perform on the test. At the end of the year she counts the number of days of school each student missed and acquires each student's test score. Which statistical procedure would you use to test the hypothesized difference in class test scores based on attendance?

High-income earners argue that they are already paying enough taxes. To test this claim, a sample of 100 high-income and 100 low-income taxpayers are asked to report their annual income and annual tax payment. A percentage of income paid in taxes is calculated for each individual. How best can we test the difference between these two samples?

Fourth grade students are given a standardized test and their scores are recorded. The next week they spend several days learning test-taking techniques. The are then given another standardized test and their scores are then recorded. Which statistical procedure will test the effectiveness of the test-taking technique instruction on standardized test scores of fourth graders?

To determine if wealthy families take longer holidays, a researcher polls 300 families at random about their annual income and the length of their last holiday. Which statistic would investigate the degree of relationship between income and length of vacation?

Answer 1

SOLUTION A: INDEPENDENT T TEST BECAUSE SAMPLES ARE INDEPENDENT AND SAMPLES ARE SUFFICIENTLY LARGE SO WE CAN ASSUME THAT SAMPLES ARE NORMALLY DISTRIBUTED.

SOLUTION B: To test the hypothesized difference in class test scores based on attendance is correlational test. Because here we are establishing correlation between class test scores based on attendance.

SOLUTION C: INDEPENDENT T TEST BECAUSE SAMPLES ARE INDEPENDENT AND SAMPLES ARE SUFFICIENTLY LARGE SO WE CAN ASSUME THAT SAMPLES ARE NORMALLY DISTRIBUTED.

SOLUTION D: PAIRED T TEST. BECAUSE HERE SAMPLES ARE MATCHED PAIR.

SOLUTION E: Correlational test statistic would investigate the degree of relationship between income and length of vacation.