# Basic Applied Statistics 200 Assignments

#### Rules

• All assignments should be your individual work; otherwise, points will be deducted. [Students who wish to work together on homework must request my permission to do so in advance.]
• Because answer keys are made available after homework is turned in, late homeworks will not be accepted. In a valid emergency, your recitation instructor may make an exception.
• Your homework should be neat and well-organized. Show your work and circle your answers. Your recitation instructor is a student like you and will not take time to decipher poor handwriting, put pages in order, or read notes scrawled in margins.
• Be sure to write or print your name at the top of the first page of your homework. Put your name or initials at the top of each additional sheet of paper or computer output. Staple your pages together.
• Answer keys are placed on file in the Math-Stat Library (4th floor Thackeray) on Monday mornings after assignments are handed in. They are on two-hour reserve so that you can take them out to be copied.
• Computer output must be circled/underlined and explained in order to receive full credit.

Note: Course average is based on 200 homework/lab points, but 240 points are possible; consider any excess as extra credit points.

#### Homework 1 Due in lecture January 24. Points shown total 18.

 [3 pts.] 1.2 (page 6) [3 pts.] 1.4 (page 8) [2 pts.] 1.6 (page 14) Suggestion: use class intervals 16-17, 18-19, etc. [3 pts.] 1.1 (page 19) [3 pts.] 1.32 (page 36) In part (a), if you split stems, you must do so consistently. For part (c),disregard the word "new". Use quartiles to find the range of the middle half. [1 pt.] 1.34 (a)(b)not(c) (page 40) [2 pts.] 1.4 (page 43) There are 9 northeastern, 12 southern states. Construct back-to-back stemplots (see 1.19 on page 23). List the Five Number Summaries and draw side-by-side boxplots. [1 pt.] 1.46 (page 45) [This question requires you to visualize the distribution of net worths. Do you believe that this distribution is skewed to the left or to the right? For the type of distribution you visualize, is the mean less or greater than the median? Now answer the question.]

#### Homework 2 Due in lecture January 31. Points shown total 15.5.

Use sketches as much as possible to solve normal problems.

 [3 pts.] 1.52 (page 51) [1.5 pts.] 1.54 (page 55) [1 pt.] 1.56 (page 56) [1.5 pts.] 1.60 (page 63) using Table A, not the 68-95 Rule [1 pt.] 1.62 (page 64) [1.5 pts.] 1.64 (page 64) [1 pt.] 1.66 (page 65) [3 pts.] 1.68 (page 65) [1 pt.] 1.81(a)(b) (page 73) [1 pt.] 1.82 (page 74)

#### Homework 3 Due in lecture February 7. Points shown total 19.5.

 [2 pts.] 2.2 (page 81) [3 pts.] 2.8 (page 91) [.5 pt.] 2.21(b) (page 103) [1 pt.] 2.33(b) (page 114) [1.5 pts.] 2.18 (page 102) [1.5 pts.] 2.20 (page 102) calculating r by hand [1.5 pts.] 2.40 (page 124) [.5 pt.] 2.58 (page 137) [.5 pt.] 2.60 (page 137) [.5 pt.] 2.62 (page 138) [4 pts.] 2.80 (page 150) [3 pts.] 2.102 (page 163)

#### Homework 4 Due in lecture Monday, February 17. Points shown total 13.5.

 [1 pt.] 3.2 (page 167) [1.5 pts.] 3.4 (page 170) [1 pt.] 3.6 (page 170) [1 pt.] 3.8 (page 173) [1 pt.] 3.2 (page 182) [1.5 pts.] 3.26 (page 184) [1 pt.] 3.4 (page 195) [I'll answer the first part for you: "The difference in earnings between the sampled men and women was so large that it would rarely occur by chance." Now you explain the results for blacks vs. whites.] [2 pts.] 3.42 (page 196) [1 pt.] 3.46 (page 200) [1.5 pts.] 3.62 (page 206) [1 pt.] 3.72 (page 209)

#### Homework 5 Due in lecture February 21. Points shown total 19.

 [1 pt.] 4.2 (page 215) [2 pts.] 4.1 (page 219) [3 pts.] 4.2 (page 226) [1 pt.] 4.24 (page 231) [3 pts.] 4.28 (page 232) [3 pts.] 4.36 (page 235) [2 pts.] 4.44 (page 247) [2 pts.] 4.48 (page 249) [To tell the distribution of a variable, report its center (mean), spread (standard deviation), and shape.] [2 pts.] 4.52 (page 249)

Don't panic if your z turns out to be very large in some of the above problems; you know about probabilities for z values outside those in Table A.

#### Homework 6 Due in lecture February 28. Points shown total 19.5.

NOTE: You are not responsible for learning how to compute binomial probabilities via the method described on pages 271-273 in your text. Most textbooks provide tables for such computations. You will, however, need to know the formulas for the mean and standard deviation of the binomial distribution (and that these formulas are only applicable when you have a binomial distribution). These will enable us to make normal approximations.

 [1.5 pts.] 5.2 (page 261) [1 pt.] 5.10 (page 267) Hint: Use Rule 3 on page 258. [1.5 pts.] 5.14 (page 267) [1.5 pts.] 5.16 (page 268) [.5 pt.] 5.18 (page 271) [3 pts.] 5.26 (page 276) [1 pt.] 5.28 (page 279) [1 pt.] 5.36(b) (page 282) [1 pt.] 5.38 (page 282) [.5 pt.] 5.40 (page 285) [1 pt.] 5.42 (page 286) [1 pt.] 5.46 (page 289) [1.5 pts.] 5.52 (page 290) Hint: for part (b), you must combine classes D and E. For part (c), compare the probability of being female, given a managerial job, to the probability of being female, given a mechanical job. Are mechanical workers just as likely to be female as managers are? [1 pt.] 5.54 (a)(c) (page 292) using a normal approximation for (c). [2.5 pts.] 5.64 (page 295) Hint: for part (a), find probabilities of positive given antibodies, negative given antibodies, positive given no antibodies, negative given no antibodies; and probability of antibodies. For (b) and (c), use the General Multiplication Rule page 284. For (d), use the Addition Rule page 258.

#### Homework 7 Due in lecture March 14. Points shown total 20.5

 [.5 pt.] 6.2 (page 303) [1 pt.] 6.4 (page 307) [1 pt.] 6.6 (page 308) [3 pts.] 6.8 (page 310) [1 pt.] 6.12 (page 312) [1 pt.] 6.14 (page 314) [3 pts.] 6.26 (page 323) Hint for (a): tell center, spread, and shape of x-bar; mark your sketch using the 68-95-99.7 Rule. [2 pts.] 6.32 (page 328) [1 pt.] 6.28 (page 325) [1 pt.] 6.3 (page 325) [3 pts.] 6.34 (page 332) Hint: you learned in Chapter 1 how to find the sample mean x-bar; just sum the data values and divide by how many there are. [3 pts.] 6.36 (page 333) by hand or with MINITAB.

#### Homework 8 Due in lecture March 21. Points shown total 11.

 [1.5 pts.] 6.38 (page 337) [1 pt.] 6.54 (page 343) [1.5 pts.] 6.55 (page 345) [1.5 pts.] 6.56 (page 345) [1 pt.] 6.58 (page 347) [1 pt.] 6.62 (page 348) [2 pts.] 6.76 (page 361) Hint: review summary of confidence interval on page 306. Think about (a) the sampling process and (b) the Central Limit Theorem. [1 pt.] 6.78 (page 361) [.5 pt.] 6.82 (page 362)

#### Homework 9 Due in lecture Monday March 31. Points shown total 10.

 [1 pt.] 7.2 (page 369) [1.5 pts.] 7.4 (page 373) [2 pts.] 7.6 (page 374) [2 pts.] 7.12 (page 382) This is a matched pairs design, looking at the mean difference from last year to this year. What is the typical Ho for matched pairs? Don't panic if your t statistic is large; you know what happens to the P-value when t is off the chart in Table C... [1 pt.] 7.14 (page 384) [1 pt.] 7.18 (page 386) Note: sample mean is 22.1, s.d. is 2.09; give a 99% confidence interval [.5 pt.] 7.25 (page 389) [1 pt.] 7.28 (page 391)

#### Homework 10 Due in lecture April 11. Points shown total 17.5.

 [1 pt.] 8.2 (page 431) [1.5 pts.] 8.4 (page 433) [1.5 pts.] 8.8 (page 436) based on the assumptions on page 435. [2 pts.] 8.1 (page 440) [1 pt.] 8.12 (page 442) [1 pt.] 8.16 (page 444) [For part (a), tell center, spread, and shape of the distribution of sample proportion.] [6 pts.] 9.2 (page 475) [2 pts.] 9.4 (page 479) [1.5 pts.] 9.6 (page 481)

#### Homework 11 Due in lecture Wednesday, April 16. Points shown total 16.

 [5 pts.] 10.2 (page 505) using MINITAB; make side-by-side boxplots instead of stemplots. [Note: plants per acre are not entered in as part of the data---they merely identify the 5 treatment groups.] [1.5 pts.] 10.4 (page 510) [1 pt.] 10.6 (page 515) [1 pt.] 11.4 (page 538) [2 pts.] 11.1 (page 546) [4 pts.] 11.12 (page 550) using MINITAB's stat>regression>regression and selecting RESULTS, which includes a table of residuals in its last option [1.5 pts.] 11.16 (page 554) do scatterplot by hand; use given output for (b) and (c)

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