STAT 200 Quiz 2 | Complete Solution

1. Which of the following are measures of central tendency? Select all that apply

1. mean
2. median
3. mode
4. Variance
5. standard deviation
6. linear transformation

2. Which of the following are measures of variability? Select all that apply

1. mean
2. median
3. mode
4. variance
5. standard deviation
6. linear transformation

3. Rachael and Peter are discussing how the mean value and variance affect the distribution graph. As the following graph shows, there are two distributions: A and B

 
Peter said that the distribution A has fatter tail because its has bigger standard deviation than the distribution B. Rachael's answer is different:she thinks the distribution A has a smaller standard deviation than the distribution B.
Who do you think is right?

1. Peter
2. Rachael
3. None of them are right. Distribution A and Distribution B have the same standard deviation

4. In a bell-shaped distribution, changing ___can make the distribution flatter (i.e. more compressed); and changing ___ can shift the distribution to the left or to the right.

1. Variance, mean
2. Mean, variance
3. Range, standard deviation
4. Mode, range
5. Mean, range
6. Mode, variance

5. A research study found that in one physics class, the correlation between pre-exam and post-exam grades was 0.90. The variance of pre-exam grades was 9 and the variance of post-exam grades was 16. Thus, the variance of the difference between pre-exam and post-exam grades is:  (show work)

6. Image that a researcher examined how the people’s heights are associated with their salaries. She found that the correlation between heights (measured in inches) and salary range (measured in dollars) was .36. Had she measured the height in cm instead, what would the correlation have been?

1. 0.36
2. 0.036
3. 3.6
4. 0.72
5. 0.18

7. The variance of X is 64 and the variance of y is 36. X and Y are independent. Thus, the sum of the variances between X and Y is:  (show work)
8. A research study found that for the new-coming medical students, the correlation between the trail Medical College Admission Test (MCAT) grades and real MCAT grades was 0.60. The variance of pre-exam grades was 81 and the variance of post-exam grades was 100. Thus, the variance of the difference between pre-exam and post-exam grades is:  (show work)

9. One of the hallmarks of the scientific method is that it depends on empirical data.

1. True
2. False

10. The best way to code a height measure of 1.8 meters would be to____

1. Have the subject write their height in inches
2. Have the subject record the information how they are comfortable, and then have the researchers convert it over to inches if necessary
3. Leave it as is; the computer understands this notation

11. If you wished to know how long since your subjects had eaten breakfast, it would be better to ask them_____

1. What time they ate their breakfast and what time it is now
2. How many minutes since they ate breakfast

12. The flaw in which a study samples too few observations from a segment of the population is called­___

1. Undercoverage bias
2. Survivorship bias
3. Self-selection bias

13. In a normal distribution, __ percentage of the area under the curve is within three standard deviations of the mean?

1. 68%
2. 50%
3. 95%
4. 99%

14. A normal distribution with a mean of 10 and standard deviation of 5. What is the corresponding Z score for a case having a value of 7?  (show work)

15. For a normal distribution with a mean of 20 and standard deviation of 2, what is the probability of getting a number greater than 26?

1. 5%
2. 2.5%
3. 1%
4. 0.5%

16. A binomial distribution is a probability distribution for ____ events for which there are ___ possible outcomes

1. Independent; two
2. Dependent; two
3. Independent; multiple
4. Dependent; Multiple

17. 
     
    
    In the figure above, what is an estimate the calories for a cereal with carbohydrate of 35 and fat of 5?

1. between 75-100
2. between 100-125
3. between 125-150
4. between 150-175
5. between 175-200
6. greater than 200

18. The contour map shown above indicates that as fat and carbohydrates increase, calories increase but not at a constant rate.

1. True
2. False

19. 
     
    
     The figure above shows...

1. data that follows the assumed distribution.
2. data that does not follow the assumed distribution.

20. The q-q plot can be used to formally test the _________ hypothesis that the data are normally distributed. This is done by computing the correlation coefficient of the n points in the q-q plot.

1. null
2. alternative