- This is the assignment for the Quiz, which will be given at the beginning of class on Wednesday May 25th. The assigned problems are not to be handed in. They are preparation for the quiz. The quiz will be multiple choice, open book and closed notes.
Read Chapter One. Everything you need to know from this chapter will also be given in lecture. You are responsible for the following concepts. Items in boldface will be covered in lecture but they are not in the text -- not in this chapter, anyway.
- Descriptive Statistics
- Inferential Statistics
- Population
- Sample
- Variable (Qualitative, Quantitative)
- Random sample
- Parameter
- Statistic
Do problems 1.2, 1.5, 1.6, 1.7, 1.11, 1.13, 1.15a-c, 1.19.
Read Chapter 2, Section 2.1. You are responsible for the following concepts.
- Class
- Class frequency
- Class relative frequency
- Class percentage
- Bar Chart
- Pie Chart
Do problems 2.5a-c; 2.7a-d; 2.11a,b,d. In class, I will also discuss frequency distributions and joint frequency distributions (See Computer Display 1); you are responsible for joint frequency distributions now. The text waits until Ch. 13.
Read Chapter 2, Section 2.2. You are responsible for the following concepts.
- Dotplot
- Stem-and-leaf display
- Bar chart
Do problems 2.25, 2.30, 2.32.
Read Chapter 2, Section 2.3. Lecture will include this material plus a couple of additional summation rules, which boil down to a+b = b+a and
a(x1+x2) = ax1 + ax2, but with funny notation. Do problems 2.43 and 2.45.
Read Chapter 2, Section 2.4. You are responsible for the following:
- Central tendency
- Symbols for the sample mean and population mean
- Skewness
Do problems 2.51, 2.53, 2.55, 2.57
Read Chapter 2, Section 2.5. You are responsible for the following:
- Variability
- Range
- Variance
- Standard deviation
- Symbols for the sample variance and standard deviation, population variance and standard deviation
Do problems 2.74, 2.75, 2.79
Read Chapter 2, Section 2.6. You are responsible for the following concepts. Don't worry; it's open book.
- Chebyshev's Rule
- Empirical Rule
Do problems 2.88, 2.89
Read Chapter 2, Section 2.7. You are responsible for the following concepts.
- pth percentile
- Sample z-score
- Population z-score
- Interpretation of z-scores for mound-shaped distributions.
Do problems 2.103-2.105, 2.107, 2.109, 2.114, 2.117
Skip section 2.8. Then read Chapter 2, Section 2.9. You are responsible for the following concepts.
- Scatterplot
- Positive relationship
- Negative relationship
Do problems 2.139,2.146
Section 2.10, which could be called how to lie with statistics, is entertaining and valuable, but you are not responsible for it. Please read it anyway.
Do all this in preparation for the Quiz on Wednesday, May 25th. The problems are not to be handed in. They are just preparation for the quiz.
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Assignment Two
This is the first of several assignments for the Midterm test, which will be on Monday June 6th. Homework questions are not to be handed in; do them in preparation for the quiz. Also, please treat all in-lecture examples as homework problems with solutions.
Read Chapter 3, Section 3.1. You are responsible for the following:
- Experiment
- Sample Point
- Sample Space
- Venn Diagrams
- Probability rules on p. 124
- Event
- Probability of ann event
- Combinations rule
- Multiplicative rule (Lecture and Section 3.8, but Section 3.8 is not assigned)
Do Exercises 3.9, 3.11, 3.13, 3.14, 3.15, 3.17, 3.27, 3.29, 3.30 (Probability of a correct match by chance is 1/3), 3.31, 3.32 (1/4, 1/2, 0),3.122, 3.123, 3.124, 3.125
Read Chapter 3, Sections 3.2, 3.3 and 3.4. You are responsible for the following:
- Union
- Intersection
- Complement
- Rule of Complements on p. 138
- Additive rule of probability on p. 139
- Mutually exclusive events (probability is zero)
Do Exercises 3.40 (3/10, 6/10, 8/10), 3.41, 3.43, 3.45, 3.47, 3.51, 3.55
Read Chapter 3, Sections 3.5 and 3.6. You are responsible for the following:
- Conditional probability formula
- Multiplicative rule of probability
- Definition of Independent Events. This definition really captures the idea of independence.
- Probability of the intersection of two independent events, page 154. In lecture and in most other texts, this is taken as the definition of independence.
Do Exercises 3.63,3.65, 3.69, 3.71, 3.73, 3.81, 3.85
Read Chapter 3, Section 3.9. You are responsible for the following:
- Bayes's Rule (Usually known as Bayes's Theorem)
Do Exercises 3.127, 3.129, 3.131, 3.133. 3.135, 3.137
Also, please do Supplemental Exercises 3.146, 3.147, 3.151, 3.161, 3.171, 3.173, 3.175
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Assignment Three
This assignment covers Chapter 4 and associated lecture material. Homework questions are not to be handed in; do them in preparation for the Midterm test, which will be on Monday June 6th. Also, please treat all in-lecture examples as homework problems with solutions.
Read the introduction to Chapter 4, and Section 4.1. You are responsible for the following:
- Discrete random variable
- Continuous random variable
Do Exercises 4.3, 4.5. Notice that in all these examples, the random variables are quantitative. But discrete random variables can be qualitative too. For example, you could randomly sample a person from the population of Toronto, and let x designate residence type: 1 = apartment, 2 = single-family dwelling, 3 = homeless and 4 = other. Can you give an example of a random variable that is both continuous and qualitative?
Read Section 4.2. You are responsible for the following:
- Probability distribution
- Two requirements satisfied by the probability distribution of any discrete random variable.
Do Exercises 4.11, 4.12 (Yes, No, No, No), 4.13, 4.15, 4.17, 4.19a and c, 4.23, 4.24 (0.51, 0.0225), 4.25.
Read Section 4.3. You are responsible for the following:
- Expected value (mean) of a discrete random variable
- Variance of a discrete random variable
- Standard deviation of a discrete random variable
- Chebyshev's rule and the empirical rule for discrete random variables
Do Exercises 4.29, 4.31, 4.33, 4.39, 4.40 (-70¢), 4.43. Note that some material has been deleted here.
Read Section 4.4. You are responsible for the following:
- Characteristics of a Binomial random variable on p. 205. These are not to be memorized, but you do need to recognize situations in which the binomial is an appropriate model. There are your guidelines.
- The reasoning behind "Deriving the binomial probability distribution"
- Formula for the binomial probability distribution on p. 208.
- Mean, variance and standard deviation of the binomial
- How to use the binomial table
Do Exercises 4.45, 4.46 (5, 0.7), 4.49, 4.51, 4.53, 4.57, 4.59, 4.61c, 4.63b, 4.66 (15), 4.68 (0.001, approximately one: calculate the z-score).
Skip Sections 4.5 and 4.6. You are done with Chapter 4.
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Assignment Four
This assignment covers Chapter 5 and associated lecture material. Homework questions are not to be handed in; do them in preparation for the final exam. Also, please treat all in-lecture examples as homework problems with solutions.
Read Sections 5.1 and 5.2 . I promise no questions about the disgusting "super weapon" on either the midterm or the final. You are responsible for the following:
- Probability density function: areas under the curve are probabilities
- Uniform probability distribution. Area = length times width.
Do Exercises 5.5, 5.9, 5.13, 5.15
Read Section 5.3 . You are responsible for the following:
- Normal distribution (bell curve) but not the formula on p. 244.
- Standard normal distribution
- How to use Table IV to get standard normal probabilities
- If X is normal, Z is standard normal; this is the "property" on p. 248
- Using the normal table in reverse
Do Exercises 5.18, 5.19, 5.22 (a: 0.0721, b: 0.0594, c: 0.2434, d: 0.3457, e: 0.5, f: 0.9233, g: 0.9901, h: 0.9901), 5.23, 5.25, 5.27, 5.29, 5.33, 5.35, 5.37, 5.43
Skip sections 5.4, 5.5 and 5.6. You are done with Chapter 5.
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Assignment Five
This assignment covers Chapter 6 and associated lecture material. Homework questions are not to be handed in; do them in preparation for the final exam. Also, please treat all in-lecture examples as homework problems with solutions.
Read the Introduction and Section 6.1. You are responsible for the following:
- Parameter
- Sample Statistic
- Sampling Distribution of a statistic.
Do Exercises 6.1, 6.3.
Read Section 6.2. You are responsible for the following:
- Point estimator
- Unbiased estimate, Biased estimate
- Standard error of a statistic
For the data of Question 6.3,
- What is µ?
- Is the sample mean x-bar biased or unbiased?
- What is the standard error of the sample mean? Show your work.
Read Section 6.3. You are responsible for the following:
- Mean and standard deviation of the sampling distribution of x-bar (p. 304)
- Central limit theorem
Do Exercises 6.21-6.24, 6.27, 6.29a and c, 6.31, 6.35, 6.37, 6.41
You are done with Chapter 6.
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Assignment Six
This assignment covers Chapter 7 and associated lecture material. Homework questions are not to be handed in; do them in preparation for the final exam. Also, please treat all in-lecture examples as homework problems with solutions.
Read the Introduction and Sections 7.1-7.2. Note that the vocabulary "target parameter" will not occur on the final exam. You are responsible for the following:
- Confidence interval: I will give a better definition in class.
- Under "Determining the target parameter," I will explain in lecture why p is a special case of µ.
- z-sub-alpha (Def. 7.4)
- Large-sample 100(1-alpha)% Confidence interval for µ, with conditions.
- Interpretation of confidence intervals (P. 327-328).
Do Exercises 7.7, 7.9, 7.11, 7.17, 7.23
Read Section 7.3. Note that this technology applies for small samples only when you have reason to believe that the data come from a normal distribution. You are responsible for the following:
- t-statistic
- Degrees of freedom
- Small-sample Confidence interval for µ, with conditions.
Do Exercises 7.29, 7.31, 7.39
Read Section 7.4. You are responsible for the following:
- p-hat. Can you see it's just x-bar, where xi is either 0 or 1?
- Sampling distribution of p-hat.
- Large-sample Confidence interval for p, with conditions.
You are not responsible for the adjusted 100(1-alpha)% Confidence interval, but it's potentially useful. Keep it in the back of your mind if you ever encounter this situation in practice.
Do Exercises 7.45(abc), 7.49, 7.57
Skip Section 4.5. You are done with Chapter 7.
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Assignment Seven
This assignment covers Chapter 8 and associated lecture material. Homework questions are not to be handed in; do them in preparation for the final exam. Also, please treat all in-lecture examples as homework problems with solutions.
Read the Introduction and Section 8.1. You are responsible for the following concepts:
- Null hypothesis
- Alternative Hypothesis
- Test statistic
- Rejection region
- Significance level (Level of significance)
- Type I error
- Type II error
The whole process is summarized nicely on P. 374 in "Elements of a test of hypothesis."
Please do Exercises 8.9, 8.11, 8.13, 8.15
Read Section 8.2. You are responsible for the following concepts:
- One-sided hypothesis and one-tailed test
- Two-sided hypothesis and two-tailed test
- Process summarized in "Large-sample test of a Hypothesis test about µ," together with conditions and possible conclusions -- p. 380-381.
Please do Exercises 8.21, 8.23, 8.25, 8.27, 8.29, 8.31, 8.33, 8.35. In 8.33, all those "explain" parts are based on the hope that you will guess the following fact: The null hypothesis H0: µ=µ0 will be rejected at significance level alpha using a two-tailed test if and only if µ0 is outside the 100(1-alpha)% confidence interval for µ. It's not really that obvious, though it does make sense.
Read Section 8.3. You are responsible for the following concepts:
- p-values
- Steps for calculating p-values
- Rejecting H0 based on a p-value.
Please do Exercises 8.37, 8.39, 8.41, 8.43, 8.45, 8.47
Read Section 8.4. This section presents the one-sample t-test.
Our text describes it as a "samll sample" test, but actually it applies to small samples from a normal distribution, and also to large samples from any distribution. For large samples from a normal distribution, it is preferable to the large-sample z-test, but you will not lose any marks in this course by using the z-test for large samples from a normal distribution.
You are responsible for the following:
- The nice summary of "Small-sample test of hypothesis about µ"
- Conditions -- which are too restrictive. Sample should be from a normal distribution, or large, or both.
- Approximating the p-value from the t table
Please do Exercises 8.55, 8.57, 8.59, 8.61, 8.63. In 8.63, assume you know that scores on the Dental Anxiety Scale have a distribution that is approximately normal. Without such assurance, you should not proceed.
Read Section 8.5.
You are responsible for the following:
- Large-sample test of hypothesis about p, including conditions.
- Finding the p-value (this is just another large-sample z-test)
Please do Exercises 8.73, 8.77, 8.79, 8.81
Skip Sections 8.6 and 8.7. You are done with Chapter 8.
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Assignment Eight
This assignment covers Chapter 9 and associated lecture material. We are skipping confidence intervals and everything concerning variances. Homework questions are not to be handed in; do them in preparation for the final exam. Also, please treat all in-lecture examples as homework problems with solutions.
Read the Introduction and Sections 9.1 and 9.2. Don't worry about confidence intervals. You are responsible for the following concepts:
- Properties of the sampling distribution of X-bar1 - X-bar2
- Large-sample test of H0: µ1 = µ2, with conditions
- p-values for this test
- Small-sample test of H0: µ1 - µ2 (Two-sample t-test), with conditions
Please do Exercises 9.3, 9.5, 9.7, 9.9a,b, 9.11, 9.15, 9.25, 9.27 (Assume a normal distribution or you can't do it). See 9.23. Why should you NOT do a t-test, as the book did?
Skim Section 9.3 or don't read it at all. You still know how to do the problems.
Please do Exercises 9.35d (assume normality), 9.39 (assume normality; why do they forget this so often?), 9.46 (again assume normality -- it's untestable with such a small sample size!)
Read Sections 9.4. Don't worry about confidence intervals. You are responsible for the following concepts:
- Properties of the sampling distribution of p-hat1 - p-hat2
- Large-sample test of H0: p1 = p2, with conditions. Condition given in class are better than those in the text. I will explain.
- p-values for this test
conditions
Please do Exercises 9.53, 9.63, 9.67
Skip sections 9.5 and 9.6. You are done with Chapter 9.
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Assignment Nine
This assignment covers a little bit of Chapter 10, along with associated lecture material. Homework questions are not to be handed in; do them in preparation for the final exam. Also, please treat the in-lecture example (see page 2 of Display 3) as a set of homework problems with solutions.
Read the Introduction and Section 10.1. You are responsible for the following concepts:
- Dependent (Response) Variable
- Factor
- Factor Level
- Designed Experiment vs. Observational experiment
- Experimental unit
Please do Exercises 10.7, 10.9
Read Section 10.2. The textbook keeps using the term "Completely randomizd design." By this, they mean either independent random sampling from two or more sub-populations (that is, pre-existing groups), or random assignment to 2 or more treatment conditions. The vocabulary "Completely randomizd design" is non-standard and you will not be tested on it, but you do have to know what they mean in order to read this part of the text.
You are responsible for the following concepts:
- Null and alternative hypotheses on p. 521
- Sum of Squares for Treatments
- Sum of Squares for Error
- Degrees of freedom, means sqares, F.
- "ANOVA F test to compare k treatments for a completely randomized design," with conditions (p. 525 )
You won't have to compute Sums of Squares by hand; final exam questions will be based on computer output .
Please do Exercises 10.19, 10.24 (a. F=4.01, b. 7, c. Yes because F > 1.98 d. p < 0.01), 10.27
Skip the rest for now, though I will discuss the Tukey tests from Section 10.3 in class. We are done!