## Math Makes Sense 6 WNCP Practice & Homework Book

Published January 1, 2009

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## Math Makes Sense 6 WNCP

by Ray Appel, Nora L. Alexander, Pearson Education Canada, Maggie Martin Connell

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- Introduction
- 1.1 Definitions of Statistics, Probability, and Key Terms
- 1.2 Data, Sampling, and Variation in Data and Sampling
- 1.3 Frequency, Frequency Tables, and Levels of Measurement
- 1.4 Experimental Design and Ethics
- 1.5 Data Collection Experiment
- 1.6 Sampling Experiment
- Chapter Review
- Bringing It Together: Homework
- 2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
- 2.2 Histograms, Frequency Polygons, and Time Series Graphs
- 2.3 Measures of the Location of the Data
- 2.4 Box Plots
- 2.5 Measures of the Center of the Data
- 2.6 Skewness and the Mean, Median, and Mode
- 2.7 Measures of the Spread of the Data
- 2.8 Descriptive Statistics
- Formula Review
- 3.1 Terminology
- 3.2 Independent and Mutually Exclusive Events
- 3.3 Two Basic Rules of Probability
- 3.4 Contingency Tables
- 3.5 Tree and Venn Diagrams
- 3.6 Probability Topics
- Bringing It Together: Practice
- 4.1 Probability Distribution Function (PDF) for a Discrete Random Variable
- 4.2 Mean or Expected Value and Standard Deviation
- 4.3 Binomial Distribution
- 4.4 Geometric Distribution
- 4.5 Hypergeometric Distribution
- 4.6 Poisson Distribution
- 4.7 Discrete Distribution (Playing Card Experiment)
- 4.8 Discrete Distribution (Lucky Dice Experiment)
- 5.1 Continuous Probability Functions
- 5.2 The Uniform Distribution
- 5.3 The Exponential Distribution
- 5.4 Continuous Distribution
- 6.1 The Standard Normal Distribution
- 6.2 Using the Normal Distribution
- 6.3 Normal Distribution (Lap Times)
- 6.4 Normal Distribution (Pinkie Length)
- 7.1 The Central Limit Theorem for Sample Means (Averages)
- 7.2 The Central Limit Theorem for Sums
- 7.3 Using the Central Limit Theorem
- 7.4 Central Limit Theorem (Pocket Change)
- 7.5 Central Limit Theorem (Cookie Recipes)
- 8.1 A Single Population Mean using the Normal Distribution
- 8.2 A Single Population Mean using the Student t Distribution
- 8.3 A Population Proportion
- 8.4 Confidence Interval (Home Costs)
- 8.5 Confidence Interval (Place of Birth)
- 8.6 Confidence Interval (Women's Heights)
- 9.1 Null and Alternative Hypotheses
- 9.2 Outcomes and the Type I and Type II Errors
- 9.3 Distribution Needed for Hypothesis Testing
- 9.4 Rare Events, the Sample, Decision and Conclusion
- 9.5 Additional Information and Full Hypothesis Test Examples
- 9.6 Hypothesis Testing of a Single Mean and Single Proportion
- 10.1 Two Population Means with Unknown Standard Deviations
- 10.2 Two Population Means with Known Standard Deviations
- 10.3 Comparing Two Independent Population Proportions
- 10.4 Matched or Paired Samples
- 10.5 Hypothesis Testing for Two Means and Two Proportions

## 11.1 Facts About the Chi-Square Distribution

11.2 goodness-of-fit test, 11.3 test of independence, 11.4 test for homogeneity, 11.5 comparison of the chi-square tests, 11.6 test of a single variance.

- 11.7 Lab 1: Chi-Square Goodness-of-Fit
- 11.8 Lab 2: Chi-Square Test of Independence
- 12.1 Linear Equations
- 12.2 Scatter Plots
- 12.3 The Regression Equation
- 12.4 Testing the Significance of the Correlation Coefficient
- 12.5 Prediction
- 12.6 Outliers
- 12.7 Regression (Distance from School)
- 12.8 Regression (Textbook Cost)
- 12.9 Regression (Fuel Efficiency)
- 13.1 One-Way ANOVA
- 13.2 The F Distribution and the F-Ratio
- 13.3 Facts About the F Distribution
- 13.4 Test of Two Variances
- 13.5 Lab: One-Way ANOVA
- A | Review Exercises (Ch 3-13)
- B | Practice Tests (1-4) and Final Exams
- C | Data Sets
- D | Group and Partner Projects
- E | Solution Sheets
- F | Mathematical Phrases, Symbols, and Formulas
- G | Notes for the TI-83, 83+, 84, 84+ Calculators

If the number of degrees of freedom for a chi-square distribution is 25, what is the population mean and standard deviation?

If df > 90, the distribution is _____________. If df = 15, the distribution is ________________.

When does the chi-square curve approximate a normal distribution?

Where is μ located on a chi-square curve?

Is it more likely the df is 90, 20, or two in the graph?

Determine the appropriate test to be used in the next three exercises.

An archeologist is calculating the distribution of the frequency of the number of artifacts she finds in a dig site. Based on previous digs, the archeologist creates an expected distribution broken down by grid sections in the dig site. Once the site has been fully excavated, she compares the actual number of artifacts found in each grid section to see if her expectation was accurate.

An economist is deriving a model to predict outcomes on the stock market. He creates a list of expected points on the stock market index for the next two weeks. At the close of each day’s trading, he records the actual points on the index. He wants to see how well his model matched what actually happened.

A personal trainer is putting together a weight-lifting program for her clients. For a 90-day program, she expects each client to lift a specific maximum weight each week. As she goes along, she records the actual maximum weights her clients lifted. She wants to know how well her expectations met with what was observed.

Use the following information to answer the next five exercises: A teacher predicts that the distribution of grades on the final exam will be and they are recorded in Table 11.27 .

The actual distribution for a class of 20 is in Table 11.28 .

d f = d f = ______

State the null and alternative hypotheses.

χ 2 test statistic = ______

p -value = ______

At the 5% significance level, what can you conclude?

Use the following information to answer the next nine exercises: The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as in Table 11.29 .

The percentage of each ethnic group in Santa Clara County is as in Table 11.30 .

If the ethnicities of AIDS victims followed the ethnicities of the total county population, fill in the expected number of cases per ethnic group. Perform a goodness-of-fit test to determine whether the occurrence of AIDS cases follows the ethnicities of the general population of Santa Clara County.

H 0 : _______

H a : _______

Is this a right-tailed, left-tailed, or two-tailed test?

degrees of freedom = _______

χ 2 test statistic = _______

p -value = _______

Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade in the region corresponding to the p -value.

Let α = 0.05

Decision: ________________

Reason for the Decision: ________________

Conclusion (write out in complete sentences): ________________

Does it appear that the pattern of AIDS cases in Santa Clara County corresponds to the distribution of ethnic groups in this county? Why or why not?

A pharmaceutical company is interested in the relationship between age and presentation of symptoms for a common viral infection. A random sample is taken of 500 people with the infection across different age groups.

The owner of a baseball team is interested in the relationship between player salaries and team winning percentage. He takes a random sample of 100 players from different organizations.

A marathon runner is interested in the relationship between the brand of shoes runners wear and their run times. She takes a random sample of 50 runners and records their run times as well as the brand of shoes they were wearing.

Use the following information to answer the next seven exercises: Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of 200 passengers is taken. Table 11.31 shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel.

State the hypotheses. H 0 : _______ H a : _______

df = _______

How many passengers are expected to travel between 201 and 300 miles and purchase second-class tickets?

How many passengers are expected to travel between 401 and 500 miles and purchase first-class tickets?

What is the test statistic?

What is the p -value?

What can you conclude at the 5% level of significance?

Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African American people, 2,745 Native Hawaiian people, 12,831 Latino people, 8,378 Japanese American people and 7,650 White people. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African American people, 3,062 Native Hawaiian people, 4,932 Latino people, 10,680 Japanese American people, and 9,877 White people. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African American people, 1,419 Native Hawaiian people, 1,406 Latino people, 4,715 Japanese American people, and 6,062 White people. Of the people smoking at least 31 cigarettes per day, there were 759 African American people, 788 Native Hawaiian people, 800 Latino people, 2,305 Japanese American people, and 3,970 White people.

Complete the table.

Enter expected values in Table 11.32 . Round to two decimal places.

Calculate the following values:

χ 2 χ 2 test statistic = ______

Is this a right-tailed, left-tailed, or two-tailed test? Explain why.

State the decision and conclusion (in a complete sentence) for the following preconceived levels of α .

- Decision: ___________________
- Reason for the decision: ___________________
- Conclusion (write out in a complete sentence): ___________________

A math teacher wants to see if two of her classes have the same distribution of test scores. What test should she use?

What are the null and alternative hypotheses for Exercise 11.43 ?

A market researcher wants to see if two different stores have the same distribution of sales throughout the year. What type of test should he use?

A meteorologist wants to know if East and West Australia have the same distribution of storms. What type of test should she use?

What condition must be met to use the test for homogeneity?

Use the following information to answer the next five exercises: Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at random and asked about the number of hours a week they work. The results are shown in Table 11.33 .

What can you conclude at the 5% significance level?

Which test do you use to decide whether an observed distribution is the same as an expected distribution?

What is the null hypothesis for the type of test from Exercise 11.53 ?

Which test would you use to decide whether two factors have a relationship?

Which test would you use to decide if two populations have the same distribution?

How are tests of independence similar to tests for homogeneity?

How are tests of independence different from tests for homogeneity?

Use the following information to answer the next three exercises: An archer’s standard deviation for his hits is six (data is measured in distance from the center of the target). An observer claims the standard deviation is less.

What type of test should be used?

Use the following information to answer the next three exercises: The standard deviation of heights for students in a school is 0.81. A random sample of 50 students is taken, and the standard deviation of heights of the sample is 0.96. A researcher in charge of the study believes the standard deviation of heights for the school is greater than 0.81.

df = ________

Use the following information to answer the next four exercises: The average waiting time in a doctor’s office varies. The standard deviation of waiting times in a doctor’s office is 3.4 minutes. A random sample of 30 patients in the doctor’s office has a standard deviation of waiting times of 4.1 minutes. One doctor believes the variance of waiting times is greater than originally thought.

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iv To the Teacher This Practice and Homework Book provides reinforcement of the concepts and skills explored in the Pearson Math Makes Sense 6 program. There are two sections in the book.The first section follows the sequence of Math Makes Sense 6 Student Book.It is intended for use throughout the year as you teach the program. A two-page spread supports the content of each core lesson in the ...

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The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0, the —null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.

2. 8-9. 1. Table 2.64 Publisher C. Find the relative frequencies for each survey. Write them in the charts. Using either a graphing calculator, computer, or by hand, use the frequency column to construct a histogram for each publisher's survey. For Publishers A and B, make bar widths of one. For Publisher C, make bar widths of two.

11.2 Goodness-of-Fit Test. Determine the appropriate test to be used in the next three exercises. 6. An archeologist is calculating the distribution of the frequency of the number of artifacts she finds in a dig site. Based on previous digs, the archeologist creates an expected distribution broken down by grid sections in the dig site.

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