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==Measures of Central Tendency== | ==Measures of Central Tendency== |

## Revision as of 02:15, 6 November 2008

## Contents

- 1 Probability and Statistics EBook Practice Problems
- 2 I. Introduction to Statistics
- 3 II. Describing, Exploring, and Comparing Data
- 4 III. Probability
- 5 IV. Probability Distributions
- 6 V. Normal Probability Distribution
- 7 VI. Relations Between Distributions
- 8 VII. Point and Interval Estimates
- 9 VIII. Hypothesis Testing
- 10 IX. Inferences from Two Samples
- 11 X. Correlation and regression
- 12 XI. Analysis of Variance (ANOVA)
- 13 XII. Non-Parametric Inference
- 13.1 Differences of Medians (Centers) of Two Paired Samples
- 13.2 Differences of Medians (Centers) of Two Independent Samples
- 13.3 Differences of Proportions of Two Samples
- 13.4 Differences of Means of Several Independent Samples
- 13.5 Differences of Variances of Independent Samples (Variance Homogeneity)

- 14 XIII. Multinomial Experiments and Contingency Tables

## Probability and Statistics EBook Practice Problems

The problems provided below may be useful for practicing the concepts, methods and analysis protocols, and for self-evaluation of learning of the materials presented in the EBook.

# I. Introduction to Statistics

## The Nature of Data and Variation

## Uses and Abuses of Statistics

## Design of Experiments

## Statistics with Tools (Calculators and Computers)

# II. Describing, Exploring, and Comparing Data

## Types of Data

## Summarizing Data with Frequency Tables

## Pictures of Data

**1. Two random samples were taken to determine backpack load difference between seniors and freshmen, in pounds. The following are the summaries: **

Year | Mean | SD | Median | Min | Max | Range | Count |

Freshmen | 20.43 | 4.21 | 17.20 | 5.78 | 31.68 | 25.9 | 115 |

Senior | 18.67 | 3.56 | 18.67 | 5.31 | 27.66 | 22.35 | 157 |

**Which of the following plots would be the most useful in comparing the two sets of backpack weights?**

**Choose One Answer:**

*A. Histograms*

*B. Dot Plots*

*C. Scatter Plots*

*D. Box Plots*

## Measures of Central Tendency

**1. Suppose that in a certain country, the average yearly income for 75% of the population is below average, what would you use as the measure of center and spread? **

**Choose one answer.**

*A. Mean and interquartile range*

*B. Mean and standard deviation*

*C. Median and interquartile range*

*D. Mean and standard deviation*

## Measures of Variation

**1. The number of flaws of an electroplated automobile grill is known to have the following probability distribution:**

X | 0 | 1 | 2 | 3 |

P(X) | 0.8 | 0.1 | 0.05 | 0.05 |

**What would be the standard deviation of the sample means if we took 100 samples, each sample with 200 grills, and computed their sample means?**

**Choose One Answer.**

*A. 0.6275*

*B. 0.0560*

*C. None of the Above*

*D. 0.89269*

**2. Suppose that in a certain country, the average yearly income for 75% of the population is below average, what would you use as the measure of center and spread? **

**Choose one answer.**

*A. Mean and interquartile range*

*B. Mean and standard deviation*

*C. Median and interquartile range*

*D. Mean and standard deviation*

## Measures of Shape

## Statistics

## Graphs and Exploratory Data Analysis

# III. Probability

## Fundamentals

## Rules for Computing Probabilities

**1. A professor who teaches 500 students in an introductory psychology course reports that 250 of the students have taken at least one introductory statistics course, and the other 250 have not taken any statistics courses. 200 of the students were freshmen, and the other 300 students were not freshmen. Exactly 50 of the students were freshmen who had taken at least one introductory statistics course.**

**If you select one of these psychology students at random, what is the probability that the student is not a freshman and has never taken a statistics course?**

*A. 30%*

*B. 40%*

*C. 50%*

*D. 60%*

*E. 20%*

## Probabilities Through Simulations

## Counting

# IV. Probability Distributions

## Random Variables

## Expectation(Mean) and Variance)

**1. Ming’s Seafood Shop stocks live lobsters. Ming pays $6.00 for each lobster and sells each one for $12.00. The demand X for these lobsters in a given day has the following probability mass function.**

X | 0 | 1 | 2 | 3 | 4 | 5 |

P(x) | 0.05 | 0.15 | 0.30 | 0.20 | 0.20 | 0.1 |

**What is the Expected Demand?**

**Choose one answer.**

*A. 13.5*

*B. 3.1*

*C. 2.65*

*D. 5.2*

## Bernoulli and Binomial Experiments

## Multinomial Experiments

## Geometric, Hypergeometric, and Negative Binomial

## Poisson Distribution

# V. Normal Probability Distribution

## The Standard Normal Distribution

## Nonstandard Normal Distribution: Finding Probabilities

## Nonstandard Normal Distribution: Finding Scores(Critical Values)

# VI. Relations Between Distributions

## The Central Limit Theorem

## Law of Large Numbers

## Normal Distribution as Approximation to Binomial Distribution

## Poisson Approximation to Binomial Distribution

## Binomial Approximation to Hypergeometric

## Normal Approximation to Poisson

# VII. Point and Interval Estimates

## Method of Moments and Maximum Likelihood Estimation

## Estimating a Population Mean: Large Samples

## Estimating a Population Mean: Small Samples

## Student's T Distribution

## Estimating a Population Proportion

## Estimating a Population Variance

# VIII. Hypothesis Testing

## Fundamentals of Hypothesis Testing

**1. Suppose you were hired to conduct a study to find out which of two brands of soda college students think taste better. In your study, students are given a blind taste test. They rate one brand and then rated the other, in random order. The ratings are given on a scale of 1 (awful) to 5 (delicious). Which type of test would be the best to compare these ratings?**

*A. One-Sample t*

*B. Chi-Square*

*C. Paired Difference t*

*D. Two-Sample t*

**2. USA Today's AD Track examined the effectiveness of the new ads involving the Pets.com Sock Puppet (which is now extinct). In particular, they conducted a nationwide poll of 428 adults who had seen the Pets.com ads and asked for their opinions. They found that 36% of the respondents said they liked the ads. Suppose you increased the sample size for this poll to 1000, but you had the same sample percentage who like the ads (36%). How would this change the p-value of the hypothesis test you want to conduct?**

**Choose One Answer.**

*A. No way to tell*

*B. The new p-value would be the same as before*

*C. The new p-value would be smaller than before*

*D. The new p-value would be larger than before*

## Testing a Claim About a Mean: Large Samples

## Testing a Claim About a Mean: Small Samples

## Testing a Claim About a Proportion

## Testing a Claim About a Standard Deviation or Variance

# IX. Inferences from Two Samples

## Inferences About Two Means: Dependent Samples

## Inferences About Two Means: Independent Samples

## Comparing Two Variances

## Inferences About Two Proportions

# X. Correlation and regression

## Correlation

**1. A positive correlation between two variables X and Y means that if X increases, this will cause the value of Y to increase.**

*A. This is always true.*

*B. This is sometimes true.*

*C. This is never true.*

**2. The correlation between high school algebra and geometry scores was found to be + 0.8. Which of the following statements is not true?**

*A. Most of the students who have above average scores in algebra also have above average scores in geometry. *

*B. Most people who have above average scores in algebra will have below average scores in geometry *

*C. If we increase a student's score in algebra (ie. with extra tutoring in algebra), then the student's geometry scores will always increase accordingly.*

*D. Most students who have below average scores in algebra also have below average scores in geometry. *

## Regression

## Variation and Prediction Intervals

## Multiple Regression

# XI. Analysis of Variance (ANOVA)

## One-Way ANOVA

## Two-Way ANOVA

# XII. Non-Parametric Inference

## Differences of Medians (Centers) of Two Paired Samples

## Differences of Medians (Centers) of Two Independent Samples

## Differences of Proportions of Two Samples

## Differences of Means of Several Independent Samples

## Differences of Variances of Independent Samples (Variance Homogeneity)

# XIII. Multinomial Experiments and Contingency Tables

## Multinomial Experiments: Goodness-of-Fit

## Contingency Tables: Independence and Homogeneity

## References

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