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# Statistics Theory True-or-False Questions

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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?

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#### Solution Preview

See attached files.

True-False (2 points)

T F 1. Statistics is a tool for turning data into information for making decisions.
True.

T F 2. Counting and categorizing are basic forms of statistics.
True.

T F 3. The mean and the median are essentially the same measures and are
interchangeable.
False: sometimes they can be similar or equal, but sometimes they can be really different. For example, find the mean and median for each of these sets of numbers:
Set 1: 1 2 5 8 9
Set 2: 1 2 5 8 200

T F 4. Samples with the same means always have the same standard deviations.
False. They can have very different standard deviations.

T F 5. The closer the kurtosis gets to 1 the better the sample.
False. Kurtosis describes the shape of the distribution of the sample (if you make a histogram). The larger the kurtosis, the more "peaked" the data. It has nothing to do with how "good" a sample is.

T F 6. A good random sample will reflect the known traits of the underlying
population.
True. This is a hard question to answer. You assume that a random sample will reflect the actual traits of the population. However, even if your sampling procedures are perfect, there is always a chance that your sample won't reflect the general population (just due to random chance, not anything that is wrong with the sample). My answer would be that a good random sample will usually approximate the known traits of the underlying population.

T F 7. A mean can be calculated for every sample.
False. It depends of the data. For example, what if your study involves asking people their favorite color? How can you take a mean if your sample consists of a list of colors?

T F 8. For a sample with a skew one correction is to trim the mean.
True. "Trimming the mean" means getting rid of the most extreme values before calculating the mean.

T F 9. The Z Score is a method for standardizing raw scores.
True. You take the raw score and convert it into what it would be if it can from a population of mean = 0 and sd = 1.

T F 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.
False. The probability of both happening can't be larger than the individual probabilities. Conditional probability is the probability of an event A, given the occurrence of another event B.

Problems/Short Answer (8 points each)

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.

The mean is the average:

mean = (5 + 6 + 3 + 6 + 7 + 2 + 10 + 5 + 4 + 12)/10
mean = 60/10
mean = 6

The median is the "middle" number. Find it by sorting the data from smallest to largest. If there are two middle numbers (like ...

#### Solution Summary

The solution provides both the calculations and worded explanations to help the reader understand each answer as well as an attached Excel spreadsheet with certain questions' working out inside.

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