Miscellanea math-341:m341-s13-hw

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Anonymous (anonymous@undisclosed.example.com) — 2013-01-01T05:53:23+00:00

Mathematics 341 - Spring 2013 Homework * Either download and install R and RStudio on your computer, and check that they work, or check that you can use RStudio on the server at http://santiago.furman.edu. * Suppose the lifetimes, in hours, of ten light bulbs were found to be 335.9, 67.5, 92.4, 189.8, 399.6, 605.5, 1133.2, 939.2, 67.7, and 31.2. Store these data in a file, use read.table() to read them into R, use summary() to find a numerical summary, and use both hist() and histogram() t…

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Anonymous (anonymous@undisclosed.example.com) — 2013-01-08T06:09:45+00:00

Mathematics 341 - Spring 2013 Homework Work through the R examples in Chapter 1.

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Anonymous (anonymous@undisclosed.example.com) — 2013-01-13T12:15:40+00:00

Mathematics 341 - Spring 2013 Homework Chapter 1 Exercises: 1.2, 1.3, 1.4, 1.6, 1.7, 1.10, 1.16, 1.17

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Anonymous (anonymous@undisclosed.example.com) — 2013-01-15T06:23:38+00:00

Mathematics 341 - Spring 2013 Homework Chapter 1 Exercises: 1.19, 1.21, 1.22, 1.23, 1.25

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Anonymous (anonymous@undisclosed.example.com) — 2013-01-17T05:38:35+00:00

Mathematics 341 - Spring 2013 Homework Suppose the lady tasting tea is asked to identify which of 20 cups of tea had the milk poured first. Again, assume the cups of tea for which the milk was poured before the tea are chosen at random by tossing a fair coin.$X$$P(X \ge x)$$x$$x = 0, 1, 2, \ldots, 20$

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Anonymous (anonymous@undisclosed.example.com) — 2013-01-23T08:04:55+00:00

Mathematics 341 - Spring 2013 Homework Chapter 2 Exercises: 2.51, 2.52, 2.54 Also: * For the lady tasting tea example, plot the power function, assuming she tastes 10 cups and we reject the null hypothesis if she identifies 8 or more cups correctly.

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Anonymous (anonymous@undisclosed.example.com) — 2013-01-24T05:48:43+00:00

Mathematics 341 - Spring 2013 Homework Chapter 2 Exercises: 2.85, 2.86 Also: In a 1958 study on the smoking habits of twins, R. A. Fisher classified 53 monozygotic (identical) twins and 18 dizygotic (fraternal) twins as having either alike or not alike smoking habits. His results were as follows:

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Anonymous (anonymous@undisclosed.example.com) — 2013-01-29T06:04:25+00:00

Mathematics 341 - Spring 2013 Homework Chapter 3 Exercises: 3.38, 3.39, 3.40, 3.41

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Anonymous (anonymous@undisclosed.example.com) — 2013-02-03T11:44:28+00:00

Mathematics 341 - Spring 2013 Homework Chapter 4 Exercises: 4.1, 4.2, 4.4. 4.9

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Anonymous (anonymous@undisclosed.example.com) — 2013-02-05T05:32:30+00:00

Mathematics 341 - Spring 2013 Homework Chapter 4 Exercises: 4.11, 4.13, 4.14, 4.15, 4.21, 4.26, 4.27, 4.28 Also: Suppose $X_1, X_2, \ldots, X_n$ is an iid random sample from exponential distribution with parameter $\lambda$. Find the sampling distribution of $\bar{X}$. Hint: First find the distribution of $\displaystyle{\frac{X_1}{n}}$

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Anonymous (anonymous@undisclosed.example.com) — 2013-02-07T07:02:28+00:00

Mathematics 341 - Spring 2013 Homework Chapter 4 Exercise: 4.30

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Anonymous (anonymous@undisclosed.example.com) — 2013-02-09T15:15:35+00:00

Mathematics 341 - Spring 2013 Homework Chapter 4 Exercises: 4.39, 4.40, 4.42, 4.44, 4.48, 4.49 Also: * When working properly, a cereal packaging machine is supposed to place 16 ounces of cereal in each box. A random sample of 10 boxes gave the following weights: 15.3, 16.1, 16.3, 15.2, 15.6, 16.4, 15.9, 15.0, 14.8, 15.1. Assuming the data are from a normal distribution, state appropriate hypotheses and perform the appropriate test. What can we conclude?

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Anonymous (anonymous@undisclosed.example.com) — 2013-02-14T05:16:48+00:00

Mathematics 341 - Spring 2013 Homework * A coin is tossed 100 times, landing heads 61 times. Find exact and approximate 80%, 90%, 95%, and 99% confidence intervals for the true probability that the coin will land head. * To determine the effect, if any, of red light on mosquitoes, 958 mosquitoes were placed in the center of a metal type which had a red light source at one end and a white light source at the other. After 2.5 minutes, 642 mosquitoes were found in the red end of the tube. Se…

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Anonymous (anonymous@undisclosed.example.com) — 2013-02-17T09:48:08+00:00

Mathematics 341 - Spring 2013 Homework Chapter 4 Exercises: 4.50, 4.54 Note: The data for 4.54 are in corn (not in gosset). See The Probable Error of a Mean by Student.

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Anonymous (anonymous@undisclosed.example.com) — 2013-02-19T05:41:45+00:00

Mathematics 341 - Spring 2013 Homework Chapter 5 Exercises: 5.1, 5.2, 5.3(a) Also: Suppose $X_1, X_2, \ldots, X_n$ is an iid random sample from a uniform distribution on the interval $[0, \theta]$. Let $Y = X_{(n)}$ be the maximum of $X_1, X_2, \ldots, X_n$. * Use the fact that $P(Y \le y) = P(X_1 \le y, X_2 \le y, \ldots, X_n \le y)$ to find the cumulative distribution function of $Y$$Y$$Y$$\theta$$k$$W = kY$$Y$$W$$W$$2\bar{X}$

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Anonymous (anonymous@undisclosed.example.com) — 2013-02-21T04:51:53+00:00

Mathematics 341 - Spring 2013 Homework Chapter 5 Exercises: 5.23(a), 5.24 Also: * Suppose $X_1, X_2, \ldots, X_n$ is an iid random sample from a uniform distribution on the interval $[-\theta, \theta]$. Find the maximum likelihood estimate for $\theta$. * Suppose $X_1, X_2, \ldots, X_n$ is an iid random sample from a uniform distribution on the interval $[\theta_1, \theta_2]$$\theta_1$$\theta_2$

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Anonymous (anonymous@undisclosed.example.com) — 2013-02-24T09:11:04+00:00

Mathematics 341 - Spring 2013 Homework Chapter 5 Exercises: 5.8, 5.9 Also: Redo Exercise 4.9 in Chapter 4, finding maximum likelihood estimates using numerical methods.

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Anonymous (anonymous@undisclosed.example.com) — 2013-02-26T05:33:09+00:00

Mathematics 341 - Spring 2013 Homework Find the Fisher information $I(\lambda)$ for an exponential distribution with rate $\lambda$.

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Anonymous (anonymous@undisclosed.example.com) — 2013-02-28T05:31:40+00:00

Mathematics 341 - Spring 2013 Homework Suppose $X_1, X_2, \ldots, X_n$ is an iid random sample from an Poisson distribution with mean $\lambda$. Let $\lambda_0 < \lambda_1$. Show that the test with significance level $\alpha$ for testing $H_0 : \lambda = \lambda_0$ versus $H_a : \lambda = \lambda_1$ specified by the Neyman-Pearson Lemma is equivalent to rejecting $H_0$$\bar{X} \ge k$$k$$P(\bar{X} \ge k \ | \ H_0) = \alpha$

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Anonymous (anonymous@undisclosed.example.com) — 2013-03-01T08:04:21+00:00

Mathematics 341 - Spring 2013 Homework Chapter 5 Exercises: 5.17, 5.18, 5.22

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Anonymous (anonymous@undisclosed.example.com) — 2013-03-10T06:55:34+00:00

Mathematics 341 - Spring 2013 Homework Chapter 5 Exercises: 5.23(b)(c)(d), 5.27 Also: A die was rolled 120 times with the following results: Number 1 2 3 4 5 6 Number of times observed 11 24 24 28 21 12 Is this a fair die? State, and test, a precise hypothesis.

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Anonymous (anonymous@undisclosed.example.com) — 2013-03-12T06:06:54+00:00

Mathematics 341 - Spring 2013 Homework Chapter 5 Exercises: 5.21, 5.23(e) Also: A newspaper article in 1965 reported that a high school student observed 9207 heads and 8743 tails in 17,950 coin tosses. * If $\pi$ is the probability of tossing a head, test the hypothesis that $H_0 : \pi = \frac{1}{2}$$\pi = \frac{1}{2}$$\frac{1}{2}$

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Anonymous (anonymous@undisclosed.example.com) — 2013-03-17T11:00:58+00:00

Mathematics 341 - Spring 2013 Homework Chapter 5 Exercise: 5.20 Also: * Test how well the verbal SAT scores in the gpa data set fit a normal distribution. * A study in 1984 examined the strength of Kevlar 49/epoxy, a material used in the space shuttle. The times to failure (in hours) of 101 strands at a stress level of 90% were found to be:

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Anonymous (anonymous@undisclosed.example.com) — 2013-03-25T12:42:05+00:00

Mathematics 341 - Spring 2013 Homework Chapter 5 Exercise: 5.28 Also: 1. Yule (in 1900) presented the following table of data on the heights of 210 married couples: Tall wife Medium wife Short wife Tall husband 18 28 19Medium husband

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Anonymous (anonymous@undisclosed.example.com) — 2013-03-21T05:15:53+00:00

Mathematics 341 - Spring 2013 Homework 1. The following data were reported in a study performed to compare the frequencies of a particular allele in a sample of subjects with adult-onset diabetes and in sample of nondiabetics: Diabetic Nondiabetic

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Anonymous (anonymous@undisclosed.example.com) — 2013-03-25T10:55:19+00:00

Mathematics 341 - Spring 2013 Homework Chapter 6 Exercises: 6.2, 6.5ab, 6.6

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Anonymous (anonymous@undisclosed.example.com) — 2013-03-27T07:23:56+00:00

Mathematics 341 - Fall 2013 Homework Chapter 6 Exercise: 6.4 Also: * The web site here has a table with the results from the lottery for the 1970 draft. Each day of the year was assigned a draft number and eligible males were drafted in the order of their birth dates. Fit a least squares line to the data and plot the line with the scatterplot of the data. Does the line indicate any trend?

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Anonymous (anonymous@undisclosed.example.com) — 2013-04-03T04:55:12+00:00

Mathematics 341 - Spring 2013 Homework Chapter 6 Exercises: 6.5c, 6.13 (note typo), 6.23 And: For the problems in Homework Set 29, test the hypothesis $H_0 : \beta_1 = 0$ and find 95% and 90% confidence intervals for $\beta_1$.

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Anonymous (anonymous@undisclosed.example.com) — 2013-04-07T10:35:57+00:00

Mathematics 341 - Spring 2013 Homework Chapter 6 Exercises: 6.10, 6.26abc, 6.32a For 6.26, 6.32, and the problems in Homework Set 29, test the hypothesis $H_0 : \beta_1 = 0$ using the analysis of variance.

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Anonymous (anonymous@undisclosed.example.com) — 2013-04-09T06:44:14+00:00

Mathematics 341 - Spring 2013 Homework Chapter 6 Exercise: 6.26de Also: For the data in Problem 2 of Homework Set 29, find * The predicted value of Young's modulus for a temperature of 825 degrees. * A 95% confidence interval for the mean modulus for a temperature of 825 degrees.

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Anonymous (anonymous@undisclosed.example.com) — 2013-04-10T12:41:54+00:00

Mathematics 341 - Spring 2013 Homework Chapter 6 Exercises: 6.16, 6.19, 6.20, 6.21, 6.27, 6.30 Also: The highest salary for a major league baseball player is given, by year, in the following table: Year Highest Salary 1985 2130300 1986 $y = ax^b$$y$$x$

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Anonymous (anonymous@undisclosed.example.com) — 2013-04-13T13:36:05+00:00

Mathematics 341 - Spring 2013 Homework Chapter 6 Exercises: 6.35 Also: * In an experiment to determine the effect of a drug on the blood glucose concentration of diabetic rats, six rats were given the drug while five others were used as controls. The blood glucose levels of the treated group (in mg/ml) were 2.02, 1.71, 2.04, 1.50, 1.83, and 1.64; for the controls, the levels were 2.15, 1.92, 1.78, 2.04, and 2.22. Assuming these samples come from normal distributions with the same variance…