Complete the following:
Response in a True or False
1. Statistics is a tool for turning data into information for making decisions.
2. Counting and categorizing are basic forms of statistics.
3. The mean and the median are essentially the same measures and are interchangeable.
4. Samples with the same means always have the same standard deviations.
5. The closer the kurtosis gets to 1 the better the sample.
6. A good random sample will reflect the known traits of the underlying population.
7. A mean can be calculated for every sample.
8. For a sample with a skew one correction is to trim the mean.
9. The Z Score is a method for standardizing raw scores.
10. The probability of event A is .3. The probability of event B is .5. If they are conditional events then the probability of both happening is .8.
Short Answer Problems:
Here are the ages of 10 children in a sample chosen from 100 total:
5, 6, 3, 6, 7, 2, 10, 5, 4, 12.
1. Find the mean, median and mode of this group.
2. Test for a skew. Is there one? If so do a 10% trim. Does that correct it?
3. Below are two data sets for investment returns on two different stocks over time.
Stock 1: 10, 12, 4, 11, 7
Stock 2: 8, 9, 10, 9, 8
Which stock has the most reliable expected return (Hint: Expected Return is the mean and reliability is measured by standard deviation)
4. We have four basic graphs in statistics: the bar, histograph, pie chart and trend line. What is the appropriate use of each one?
5. How does probability with replacement differ from probability without replacement?
6. A tank of fuel allows an airplane to travel an estimated 700 miles although head winds and tail winds can alter the actual range and the standard deviation is 40 miles. What is the probability a plane will be able to travel 775 miles on one tank of fuel?
7. You are examining a sample of IQ scores with a mean of 115 and a standard deviation of 12. Find the actual IQ score that corresponds with the following Z scores:
a. 1.60
b. -.95
c. 2.5
d. -.1
8. In 1980 a certain student scored a 1270 on his SAT in a year when the mean was 1010 and the standard deviation was 90. In 2010 this student's daughter scored a 2050 in a year when the mean was 1510 and the standard deviation was 160. Who did better? (Hint the Z Score will be useful)
9. A student has a 3.35 GPA which is at the 75th percentile. The standard deviation is .55. Find:
a. The mean
b. The percentile of a student with a 2.80 GPA
c. Is this school too easy or hard? Why?
10. The management and labor union are in salary negotiations. The union wants a salary increase in the new contract and management does not. When citing "the average salary" in this firm compared to "the average salary of a union worker" which side of the negotiation is likely to use the mean and which will use the median and why?