What kind of relationship does a correlation coefficient test?

Learning Objectives:

• Learn the difference between Type I errors and Type II errors
• Learn the steps used to apply a statistical test to test any null hypothesis
• Learn what confidence intervals are.

1. An employer chose to test his employees for heroin use with an opiate urine test. One employee, Monica, had eaten poppy seed bagels, which caused her to test positive for opiates (even though she had never used heroin). The employer fired her for using heroin. Circle the best description of the employer’s conclusion, below. (2 points)

Type I Error (False Positive)    Type II Error (False Negative)     Correct Conclusion

2. A woman takes a home pregnancy test because she fears she may be pregnant. She actually is pregnant, but she hasn’t been pregnant long, so the test says that she is not pregnant. She concludes that she is not pregnant. Circle the best description of her conclusion, below. (2 points)

Type I Error (False Positive)    Type II Error (False Negative)     Correct Conclusion

3. A researcher compares two methods for quitting smoking. Method A is using self-help group and Method B is using the eCigarette. The self-help group actually works better than the eCigarette, but when the researcher runs the statistics, she finds there is no difference between Method A and Method B. Circle the best description of the researcher’s conclusion below. (2 points)

Type I Error (False Positive)    Type II Error (False Negative)     Correct Conclusion

4. Which is wider, a 95% confidence interval or a 99% confidence interval? Explain why? (2 points)

5. We conducted a research study and found that the average number of times students in HESC 349 ate fast food per week was 4.0. The 95% confidence interval was (3.5, 4.5). Interpret these findings (that is, explain what they mean). (2 points)

6. You are studying the amount of sodium in Dill pickles. Your null hypothesis is that the average amount of sodium per pickle in a case of pickles=12mg. You run the data in SPSS using a 5% alpha level, and your output tells you: p=.0287. What does this mean? (2 points)

7. You are studying the amount of sodium in two different brands of pickles. Your null hypothesis is that M₁=M₂ (or M₁-M₂=0). You run the data using a 5% alpha level in SPSS, and your output tells you that p=.17. What does this mean? (2 points)

8. Imagine that a large, private University in California claims the average SAT score for incoming freshman is 2000, but we suspect that the University is inflating the average. To test the University’s claim, we take a random sample of 100 students and find their average to be only 1985, with a SD of 110. (6 points)

1. Formulate a null and research hypothesis to test our hypothesis that the mean SAT score is actually less than 2,000

Ho:

H1:

1. Calculate the Z statistic

1. Is this a directional or non-directional test?
2. What is alpha?
3. What is/are the critical values?
4. What is your decision?
5. What is your conclusions?

9. If you are calculating a correlation coefficient testing the relationship between height and weight, state the null and research hypotheses. (3 points)

Null:

Research:

1. What kind of relationship does a correlation coefficient test?

1. What does a “perfect negative correlation” mean?

1. What number will your correlation coefficient be close to when there is no particular pattern of relationship between your two variables?

10. Interpret the correlation coefficient in the scatterplots below. (2 points)