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# Descriptive Statistics and hypothesis testing

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1. Suppose that a broad cross section of high school students took a very difficult scholarship exam and almost all scored very low but a very small number scored very high. When plotted as a curve, the distribution will show what type of skew?

2. Which type of distribution is often found in the nature?

3. What is the formula for the mean(M)?

4. What are the most commonly used symbols for mean in academic journals?

5. If you read that 20% of a population of 1,000 was opposed to a city council resolution, how many are opposed?

6. What levels of measurements are used for parametric statistics?

7. Find the mode of the following scores

11, 13, 16, 16, 18, 21, 25

8. In a distribution with a negative skew, does the mean or median have higher value?

9. Find the median of the following scores

9,7,10,4,8,6

10. If the median price of a house in Mudsville is 125,000, what percentage of the houses cost more than 125,000?

11. If you read the following statistics in a report, which group should you conclude has the greatest variability?

Group A M= 3.23 SD = 2.14

Group B M= 25.99 SD= 3.01

Group C M =22.43 SD = 4.79

12 What is the outliers in the following set of scores?

50,50,52,53,56,57,75

13What is the value of SD for the scores shown below?

5, 4,6,8,2

14. If M = 52.0 and SD =4.0 for a normal distribution, between which two values do 68% of the cases lie?

15. If you go out two SD units on both sides of the mean, you will gather up what percentage of

cases?

16. If M= 133.9 and SD= 20.5, what percentage of the cases in a normal distribution lies between scores of 113.4 and 154.4?

17. If M = 30.0 and SD =6.0 for a normal distribution, between which two values do 99.7% of the cases lie?

18. If you go out on SD unit on both sides of the mean, you will gather what percentage of the cases?

19. Find the value of the range of scores below (all steps should be clearly shown for full credits)

8, 9, 12, 7, 10, 6, 11, 31
20. What is the name of the score that is much higher or much lower than the other scores?

21. Which average is defined as the middle score?

22. What percentile rank is the same as the median?

23. A study was done on survival time for 10 patients following a new treatment for cancer. The time in months were: 24, 8, 12, 3, 20, 18, 24, 19, 27, 25

Find the:

a. Mean

b. Median

c. Mode

d. Variance

e. Standard deviation

24. In an experiment designed to answer questions about cause and effect, data about the effect would be which variable?

25. What Statistic do you need before you can arrive at deviation score?