1. In your own words, what does a z-score tell us about a raw score?

2. What does it mean if a Z score is negative?

3. Are there any limits to how large or small a Z score can be, in theory?

4. What values does most of the z-score distribution lie between?

5. A dataset has a mean of 40.22 and a standard deviation of 3.61. The dataset is transformed into a z-distribution. What are the mean and standard deviation of the transformed data set? 

6. Three students take the same test. The mean is 75, and the standard deviation is 8.

A’s raw score is 78.

B’s z-score is -.32.

C’s raw score is 3.7 raw points above the mean.

Which student had the highest score? (Hint: transform them into scores to compare).

7. You should have the formula for calculating Z to answer these problems. The data are test scores from a chemistry class with 5 students. The data are a “population.” The mean is 79.6 and the standard deviation is 11.55. Calculate each student’s z-score from the raw scores given. Raw scores: 

76

98

80

62

82

a. What is the z-score for the raw score of 76? 

b. What is the z-score for the raw score of 98?

c. What is the z-score for the raw score of 80?

d. What is the z-score for the raw score of 62?

e. What is the z-score for the raw score of 82?

Chapter 6

You will find the empirical rule useful for these exercises. For your own practice I strongly recommend “sketching” each problem by drawing a little distribution and marking off, generally, the location of scores. 

1. In a data set with a mean of 20 and a standard deviation of 5, what is the chance of

Having a score greater than 30?

2. In that same data set, what is the chance of being between the scores of 10 and 15?

3. If I have a data set with a mean of 25 and a SD of 3, would you accept or reject the claim that a value of 30 probably comes from this data set?

4. If I have a data set with a mean of 40 and a SD of 8, would you accept or reject the claim that a value of 22 came from this data set?

5.  Assume the lines in the graph mark off standard deviations from the mean. Using the insert shape function draw an arrow or arrows identifying the line that marks the cutoff for concluding that there is a 5% chance that my value is not in the data set. 

6. If I had a data set with a mean of 50 and a standard deviation of 6, what values above and below the mean mark the cutoff for concluding a value is not in that data set? 

7. I have a sample value of 40. I know the standard deviation of the null population is 4. What would the mean or means of a null population have to be for me to conclude that my sample value is NOT from the null population?

8. A car manufacturer claims their car gets 50 mpg. I collect a sample and find that my sample of cars gets on average 45 mpg. Why can’t I just say that the two numbers are different, and therefore my sample data are different from the population data?

9. Why do we need to relate data to probability in hypothesis testing?

10. A milk company claims that their milk sells for 3 dollars a gallon, with a standard deviation of 75 cents. I collect a sample and find that in my sample milk costs 4.75 a gallon.  Find the Z score and tell me whether or not I can reject the manufacturer claim.

11. A medication manufacturer claims their meds reduce depressive symptoms by 10 points, with a standard deviation of 2 points. I think it is probably not that good. I collect data and find that in my sample symptoms are reduced by 6 points. Find the Z score and tell me whether or not I can reject the manufacturer claim.