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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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Statistics General Questions: 20 True or False questions and 20 multiple choice questions.

See the attached file for table format.

Statistics - 40 General Questions

True/False - Please type True or False in the box to the right of the statement.

1 Based on a classical approach, the probability of an event is defined as the number of favorable outcomes divided by the total number of possible outcomes.
2 One characteristic of the F distribution is that F cannot be negative.
3 If the null hypothesis states that there is no difference between the mean net income of retail stores in Chicago and New York City, then the test is two-tailed.
4 Hypothesis testing is a procedure that uses sample evidence and probability theory to decide whether to reject or fail to reject a hypothesis.
5 The probability of rolling a 3 or 2 on a single die is an example of mutually exclusive events.
6 If the computed value of F is 0.99 and the critical value is 3.89, we would not reject the null hypothesis.
7 If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population.
8 As sample sizes decrease, we are more confident in sample estimates of population parameters.
9 A probability of 0.0 is assigned to an event that is certain not to occur.
10 To apply the special rule of addition, the events must be independent.
11 As sample sizes decrease, rejecting the null hypotheses is less likely.
12 An alternate hypothesis is a statement about a population parameter that is accepted when the null hypothesis is rejected.
13 Type II error is the probability or risk of rejecting a null hypothesis when it is actually true.
14 If the null hypothesis is true and the researchers do not reject it, then a correct decision has been made.
15 The fifth and final step in testing a hypothesis is taking a sample and, based on the decision rule, deciding if the null hypothesis should be rejected.
16 You can forecast benefit costs with 100% accuracy using time series regression analysis.
17 A standard distribution has more than one peak.
18 You can only forecast benefit costs within a certain amount of confidence interval using time series regression analysis.
19 Aren't you glad this class is over.
20 A standard distribution looks like a bell.

Multiple Choice - Type in the letter in the left side box that corresponds to the correct answer.

1 Which of the following is NOT one of the five steps in the hypothesis testing procedure?

A. Formulate a decision rule
B. State the null and alternate hypotheses
C. Select a level for 
D. Identify the test statistic

2 What is a Type II error?

A. Accepting a false null hypothesis
B. Rejecting a false null hypothesis
C. Accepting a false alternate hypothesis
D. Rejecting a false alternate hypothesis

3 What is the level of significance?

A. Probability of a Type II error
B. Probability of a Type I error
C. z-value of 1.96
D. Beta error

4 Administering the same test to a group of 15 students and a second group of 15 students to see which group scores higher is an example of

A. a one sample test of means.
B. a two sample test of means.
C. a paired t-test.
D. a test of proportions.

5 Given the following regression model, which factor do you think is most important in predicting benefit costs?

Benefit costs = 0.9(employee population) +
0.8(claims experience) + 0.4(gender)

A. employee population
B. claims experience
C. gender
D. cannot be determined

6 Your assistant has determined that the regression model that best describes the relationship between performance (x) and salary (y) is:
y = 7.107 + 0.813x

How may this regression model be useful to you?

A. It shows that performance and salary move in opposite directions.
B. It can be used to determine the appropriate salary, given performance.
C. It can be used to determine performance given salary.
D. There is no relationship

7 What is the logarithm in the equation 109 = 1,000,000,000?

A. 10
B. 9
C. 1,000,000,000D. 1

8 In executive compensation, it is important to consider distributions because:

A. Most wage earners receive salaries on the lower end of the scale.
B. Low salaries throw the mean salary level off.
C. No company wants to pay above the market level.
D. None of the above.

9 The information in the data that is not explained by the regression model is called:

A. Hats
B. Estimates
C. Residuals
D. Curves

10 Collinearity occurs when:

A. independent variables are highly correlated with each other
B. all coefficients are large
C. independent variables are highly correlated with the dependent variable
D. None of the Above

11 Given the information below, what is the cost-of-living index of Oregon?

City Income ($)*
National 35,973
Michigan 35,862
Florida 36,985
Oregon 33,044

*The numbers are used for illustration purposes only.

A. 82
B. 92
C. 109
D. 33,044

12 Which statement is correct about the F distribution?

A. Cannot be negative
B. Cannot be positive
C. Is the same as the t distribution
D. Is the same as the z distribution

13 The result of a particular experiment is called a(n)

A. observation.
B. conditional probability.
C. event.
D. outcome.

14 What do we call the statement that determines if the null hypothesis is rejected?

A. Decision rule
B. Test statistic
C. Alternate hypothesis
D. Critical value

15 What is another name for the alternate hypothesis?

A. Null hypothesis
B. Hypothesis of no difference
C. Rejected hypothesis
D. Research hypothesis

16 Which approach to probability assumes that the events are equally likely?

A. Classical
B. Empirical
C. Subjective
D. Mutually exclusive

17 Using the median test only, is there a difference in compensation between the following 2 groups?

Protected Non-protected
1 $20,746 $20,972
2 $21,356 $21,864
3 $22,018 $22,808
4 $22,900 $22,900
5 $24,986 $25,087
6 $25,983 $26,076
7 $26,385 $27,476

A. There is a substantial difference in the medians of the 2 groups.
B. There is a small difference in the medians of the 2 groups.
C. There is no difference in the median value between the 2 groups.
D. Not enough information to make a determination.

18 To set executive pay using regression analysis, what is the first step you must take?

A. Identify the factors used in establishing compensation levels.
B. Find the regression equation.
C. Do a benchmark study.
D. Set you salary ranges.

19 The best way to determine employee benefit preferences is to use:

A. Benchmarking
B. Surveys
C. Chi-square test
D. Regression analysis

20 To conduct a test of hypothesis with a small sample, we need to be able to make an assumption that:

A. a larger computed value of t will be needed to reject the null hypothesis.
B. the region of acceptance will be wider than for large samples.
C. the confidence interval will be wider than for large samples.
D. the population is normally distributed.

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