# 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 points, but 250 points are possible; consider any excess as extra credit points.

#### Homework 1 Due in lecture January 25. Points shown total 28.

 [3 pts.] 1.2 (page 6) [3 pts.] 1.4 (page 8) [2 pts.] 1.8 (page 14) For part (d), you must approximate the histogram area to the left of 0, where total area is 100%. [3 pts.] 1.10 (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.] 1.40 (page 43) There are 9 northeastern, 12 southern states. Construct back-to-back stemplots (see 1.19 on page 23). List the Five Number Summary 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.] [5 pts.] #1 (student data) [5 pts.] #2 (student data)

Student Data Problem #1: Pick a quantitative variable from those in the list of surveyed information (height; shoesize; gender; parent height; preferred color; weight; major; credits; year at Pitt; on or off campus (mode of transport); time spent: exercising, on computer, watching TV, doing homework, sleeping; age; parents' ages; siblings; smoking habits; earnings; left- or right-handed; random number).

1. Before you even look at the data, write a sentence or two telling what you expect you might see in terms of center, spread, and shape of the distribution. Mention mean and standard deviation, as well as median and range. Are outliers likely?
2. Using MINITAB, produce descriptive statistics and displays for the variable you selected.
3. Summarize your results in terms of center, spread, shape (outliers?); are results close to what you anticipated?

Student Data Problem #2: Pick a quantitative and a qualitative variable from those in the list of surveyed information, so that you can compare values of the quantitative variable for two or more groups.

1. Before you even look at the data, write a sentence or two telling how you think centers, spreads, and shapes of the distributions will compare.
2. Use MINITAB to unstack the quantitative values according to the groups of interest. Then produce descriptive statistics and side-by-side boxplots.
3. Summarize your results; are they close to what you anticipated?

#### Homework 2 Due in lecture February 1. 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 8. Points shown total 29.5.

 [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 [5 pts.] #3 (student data) [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) [5 pts.] #4 (student data) [4 pts.] 2.80 (page 150) [3 pts.] 2.102 (page 163)

Student Data Problem #3: Pick two quantitative variables from those in the list of surveyed information, and consider the relationship between them. Decide if there is an obvious choice for which is explanatory (x) and which is response (y).

1. Before you even look at the data, write a sentence or two telling what kind of relationship you expect to see. Include mention of direction, form, strength and possible outliers.
2. Use MINITAB to display the relationship with a scatterplot. If it appears to be linear, produce the regression line and find the correlation.
3. Summarize your results in terms of direction, form, strength, outliers and/or influential observations.

Student Data Problem #4: Pick two qualitative variables from those in the list of surveyed information, and consider the relationship between them. (You may want to avoid considering a variable that has too many different possible values, like major. One option is to allow for fewer categories, such as major declared or not.) Decide on an assignment of which variable is explanatory and which is response.

1. Before you even look at the data, write a sentence or two telling what kind of relationship you expect to see: should the variables be independent? If not, for which explanatory value do you expect to see a higher proportion in the response of interest?
2. By HAND or with MINITAB, produce a two-way table, then compare proportions in the category of interest; display your results with an appropriate bar graph.

#### Homework 4 Due in lecture February 18. Points shown total 13.5.

 [1 pt.] 3.2 (page 167) [1 pt.] 3.6 (page 170) [1 pt.] 3.8 (page 173) [1.5 pts.] 3.18 (page 182) [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 22. 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) [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 March 1. Points shown total 18.

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) [1.5 pts.] 5.26 (page 276) [1 pt.] 5.28 (page 279) [1 pt.] 5.34(a)(b) (page 281) [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 15. Points shown total 27.

 [.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) [5 pts.] #5 (student data) [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.] 6.30 (page 325) [3 pts.] 6.34 (page 332) [4.5 pts.] 6.36 (page 333) using MINITAB.

Student Data Problem #5: Pick a quantitative variable from those in the list of surveyed information, and consider its mean value for the population of survey respondents (all students in my Stat classes this semester). Avoid variables (like "earnings") whose distribution would be far from normal.

1. Before you even look at the data, give a rough guess for the population mean.
2. Use MINITAB to discover the population standard deviation (sigma). [Try to ignore the population mean, which is assumed to be unknown in this problem.] Take a medium-sized random sample (20 to 30 values) and use it to produce a confidence interval for "unknown" population mean based on a standard normal (z) test statistic.
3. State your results; is the confidence interval consistent with your rough guess for population mean?

#### Homework 8 Due in lecture March 22. Points shown total 16.

 [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) [5 pts.] #6 (student data) [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)

Student Data Problem #6: Pick a quantitative variable from those in the list of surveyed information and consider its mean value for the population of survey respondents (all students in my Stat classes this semester). Avoid variables (like "earnings") whose distribution would be far from normal.

1. Before you even look at the data, formulate a null and alternative hypothesis about population mean value.
2. Use MINITAB to discover the population standard deviation (sigma). [Try to ignore the population mean, which is assumed to be unknown in this problem.] Take a random sample of about 20 to 30 values and carry out a test of your hypotheses based on a standard normal (z) test statistic.
3. State your results: based on the p-value, decide whether or not to reject the null hypothesis; finally, draw conclusions about the "unknown" population mean of interest.

#### Homework 9 Due in lecture April 1. Points shown total 30.

 [1 pt.] 7.2 (page 369) [1.5 pts.] 7.4 (page 373) [2 pts.] 7.6 (page 374) [5 pts.] #7 (student data) [2 pts.] 7.12 (page 382) 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) [5 pts.] #8 (student data) [1 pt.] 7.20 (page 386) [.5 pt.] 7.25 (page 389) [1 pt.] 7.28 (page 391) [5 pts.] #9 (student data) [5 pts.] #10 (student data)

Student Data Problem #7: Pick a quantitative variable (from those in the list of surveyed information) whose values have been recorded in pairs (eg. ages of mothers and fathers, or heights of male/female students and their fathers/mothers).

1. Before you even look at the data, formulate null and alternative hypotheses about the population mean difference. [The null hypothesis may state that this difference is zero.]
2. Use MINITAB to take a random sample of data pairs and use a paired-sample procedure to test your hypotheses.
3. State your results: based on the p-value, decide whether or not to reject the null hypothesis; finally, draw conclusions about the population mean difference.

Student Data Problem #8: Pick a quantitative variable from those in the list of surveyed information, and consider its mean value for the population of survey respondents (all students in my Stat classes this semester).

1. Before you even look at the data, formulate a null and alternative hypothesis about the population mean value.
2. Proceed as if you did not have access to the population standard deviation (sigma). Take a random sample of about 20 to 30 values and carry out a test of your hypotheses based on a t test statistic. If your alternative was two-sided, simply circle the confidence interval as given in the output. If your alternative was one-sided, carry out a two-sided procedure to produce a confidence interval (and circle it). Plot the data and discuss robustness according to the guidelines on page 380.
3. State your results: based on the p-value, decide whether or not to reject the null hypothesis; finally, draw conclusions about the "unknown" population mean of interest.

Student Data Problem #9: Pick a quantitative variable (from those in the list of surveyed information) and a qualitative variable which allows for two possible values, so that you can compare values of the quantitative variable for two groups.

1. Before you even look at the data, give a rough guess for the difference between population means of the two groups. If you can't be more specific, at least state whether you think the confidence interval for difference between population means will contain zero, or only negative numbers, or only positive numbers.
2. Use MINITAB to unstack the quantitative variables according to the groups of interest. Take independent random samples of about 10 or 15 from each group and examine sample standard deviations to decide whether or not to use a pooled procedure. Then set up a confidence interval for the difference between population means. Include side-by-side boxplots.
3. State your results; is the confidence interval consistent with your expectations?

Student Data Problem #10: Pick a quantitative variable (from those in the list of surveyed information) and a qualitative variable which allows for two possible values, so that you can compare values of the quantitative variable for two groups.

1. Before you even look at the data, state a null and alternative hypothesis about the difference between population means of the two groups. [The null hypothesis typically states that the difference is zero.]
2. Use MINITAB to unstack the quantitative values according to the groups of interest. Take independent random samples of about 10 or 15 from each group and examine sample standard deviations to decide whether or not to use a pooled procedure. Then test your hypotheses. Include side-by-side boxplots.
3. State your results: based on the p-value, decide whether or not to reject the null hypothesis; finally, draw conclusions about the difference between population means.

#### Homework 10 Due in lecture April 12. Points shown total 27.5.

 [1 pt.] 8.2 (page 431) [1.5 pts.] 8.4 (page 433) [2 pts.] 8.6 (page 434) [1.5 pts.] 8.8 (page 436) based on the assumptions on page 435. [5 pts.] #11 (student data) [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) [5 pts.] #12 (student data)

Student Data Problem #11: Pick a qualitative variable from those in the list of surveyed information, and have in mind a particular category of interest.

1. Before you even look at the data, give a rough guess for the population proportion falling into the category of interest. Then formulate a null and alternative hypothesis about the population proportion in that category.
2. Use MINITAB to take a random sample of values. By HAND or using MINITAB, set up a confidence interval for "unknown" population proportion, and test your hypotheses.
3. State your results: based on the p-value, decide whether or not to reject the null hypothesis; finally, draw conclusions about the "unknown" population proportion of values falling into the category of interest.

Student Data Problem #12: Pick two qualitative variables from those in the list of surveyed information.

1. Before you even look at the data, formulate a null and alternative hypothesis about the relationship between those two variables.
2. You may use MINITAB to take a random sample of data pairs, or work with the entire population of data pairs. By HAND or with MINITAB, construct a two-way table of counts occurring in each category combination, then carry out a chi-square test.
3. State your results: based on the p-value decide whether or not to reject the null hypothesis; finally, draw conclusions about whether or not the variables are related.

#### Homework 11 Due in lecture April 17. Points shown total 26.

 [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) [5 pts.] #13 (student data) [1 pt.] 11.4 (page 538) [2 pts.] 11.10 (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) [5 pts.] #14 (student data)

Student Data Problem #13: From the list of surveyed information, pick a quantitative variable and a qualitative variable which allows for MORE than two possible values, so that you can compare values of the quantitative variable for several groups.

1. Before you even look at the data, state a null and alternative hypothesis about the populatin means for those groups.
2. Use MINITAB to unstack the quantitative values according to the groups of interest. Take independent random samples of about 5 from each group and examine sample standard deviations to verify that the assumptions of ANOVA are satisfied; produce the ANOVA table in MINITAB. Include side-by-side boxplots.
3. State your results: based on the p-value, decide whether or not to reject the null hypothesis; finally, draw conclusions about the population means of interest.

Student Data Problem #14: Pick two quantitative variables from those in the list of surveyed information, and consider the relationship between them. Decide if there is an obvious choice for which is explanatory (x) and which is response (y).

1. Before you even look at the data, state a null and alternative hypothesis about the slope beta of the regression line.
2. Use MINITAB to take a random sample of 20 to 30 data pairs, then verify that their scatterplot appears linear. Carry out a regression.
3. State your results: First, use the output to estimate the regression model parameters alpha, beta, and sigma. Then, based on the p-value, decide whether or not to reject your null hypothesis; finally, draw conclusions about the relationship between populations of x and y values.

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