Problems are from:
Shafer and Zhang, Introductory Statistics
1. If there are 27 yellow balloons, 37 green balloons, 13 blue balloons, and 43 Panther purple balloons, convert these frequencies to relative frequencies.
27/(27+37+13+43) = .23, 37/120 = .31, 13/120 = .11, 43/120 = .36
2. Which of the following information about the Ivy League Schools could be displayed in a pie chart with one wedge per school.? a) tuition (cost of attendance) b) number of students c) endowment of the schools d) school mascot e) percentage of minority students f) undergraduate gpa
b (number of students), c (endowment)
p.8 - 10
quantitative (a,b); qualitative (c); technically quantitative, but you should not analyze ththe data that way (d,e)
p.14 - 1, 3
p.22 - 2, 3, 9, 11
2 - It is easier to construct, you can recover all the original data
For problem 3 above, how many classes do you have, and what are the class sizes?? [6 classes with 10 units each] What are the class marks? [55 or 55.5, 65 or 65.5, etc.] class boundaries? [50, 60, 70, etc. or 50.5, 60.5, 70.5, etc. ] If you wanted to have three classes (categories) what class size should you use [(100-52)/3 = 18, so 15 or 20], and what would be your class marks and boundaries [perhaps marks 55, 70, 85, 100 with boundaries 47.5, 62.5, 77.5. 92.5 107.5]? If you wanted to have 7 classes, what class size should you have [(100-52)/7 = 6.86, so 5 or 8 or 10], and what would be your class marks and class boundaries? [perhaps marks 54, 62, 70, 78, 86, 94, 102 with boundaries 50, 58, 66, 74, 82, 90, 98, 106 and use left endpoint inclusion
p.42 - 1, 5 (also find the midrange - 4), 7, 13 (also find the midrange - (132+160)/2=146), 19, 21 (also find the midrange - (26+32)/2=29)
p.57 - 3, 5, 7, 13
p.70 - 3 (also find the 20th and 60th percentiles - .20*71 = 14.2, so choose the 15th datum which is 56; .60*71 = 42.6, so choose the 43 datum, which is 76 (there are 71 data)), 7, 9, 15, 19, 21, 26 - -1.19 is negative, so Dromio's score is below the mean; 49.6-1.19*1.35=48, 29, 31, 37
p.90 - 1, 5, 7, 9
For a histogram with class marks (and bar heights): 125 (12), 150 (32), 175 (28), 200 (7), what are greatest and least possible values for the mean and median of the underlying data? [the data in each class can be anywhere between the lower and upper class boundaries, so the mean is between (12*112.5+32*137.5+28*162.5+7*187.5)/(12+32+28+7)=147 and (12*137.5+32*162.5+28*187.5+7*212.5)/(12+32+28+7)=172; there are 79 data, hene the median is the value of the 40th datum, the 40th datum is in the 150 class, so the median is between 137.5 and 162.5] What is the 'best' estimate for the mean? [The 'best' estimate for the mean is equivalent to putting all the data at the class marks, hence 159.5] What is the 'best' estimate for the median? [equal area under the histogram either side of the median provides 79*25/2=987.5; 987.5-12*25=687.5; 687.5/32=21.48; 137.5+21.48=158.98]
[First test]
p.106 - 3, 7, 11, 13, 17, 21
p. 125 - 5, 7, 11, 15
p.148 - 1, 3, 5, 7, 9, 11, 13, 22 - I assigned this to remind you that rolling two dice entails 6*6=36 equally likely events; N: {36, 45, 54, 63, 46, 55, 64, 56, 65, 66}, T: {21, 22, 23, 24, 25, 26, 12, 32, 42, 52, 62}, F: {51, 52, 53, 54, 55, 56, 15, 25, 35, 45, 65}, a) 10/36=.28, b) 5/11=.45, c) 2/11=.18, d) no, no, 24 - a) 1-.002^2 = .999996; b) .998^2 = .996004
p. 160 - 1
p. 174 - 1, 3, 9 (you must also assume independence)
If there are 7 students in a class, how many ways can you choose a president, vice-president, and secretary-treasurer? [7*6*5 = 210] If there are seven students in a class, how many ways can you choose a committee of three? [7*6*5/(3*2*1) = 35] If there are four boys and three girls in a class, how many different orders of gender are possible (i.e., how many different arrangements are there of the letters MMMMFFF)? [7!/(4!3!) = 35]
p. 195 - 1, 3, 5 (do not use the tables), 9, 15, 18 [a) (1-.025)^12 = .74, b) i) 1-.74 = .26, ii) 1-.74-12*.025*/975^11 = .035 ]
p. 212 - 3, 9
p. 221 - 1, 3, 7
p. 231 - 1, 3, 11, 15
p. 247 - 1, 5, 7, 9, 11, 23
If 70% of voters like Alfred, what is the probability that more than 60 voters in a random sample of 80 voters will like Alfred? [(60.5-.70*80)/(80*.7*.3)^.5 = 1.10 ; 1.10 -> .8643 (from table), 1-.8643 = .14]
p. 255 - 1, 3
p. 267 - 1, 3, 5, 15
[second test]
p. 280 - 3, 5, 7, 13, 15, 17 [I shall cover this section with confidence intervals for proportions (section 7.3, p. 312); I included problems 13, 15, 17 so you will know that data and questions can be expressed either in terms of proportions or raw count, but you must convert everything to proportions (or everything to raw count) to solve the problem]
p. 294 - 1, 3, 5, 7
p. 304 - 1 (I do not cover the t-distribution, this is a reminder that if the population standard deviation sigma is known, you use the normal distribution no matter how small n is if the underlying population is normal)
p. 314 - 1, 5, 7, 9
p.328 - 1, 3, 5, 7
p. 344 - 1, 3
p. 351 - 1, 3, 5, 7, 9, 19
p. 364 - 1, 5, 7, 9 (also construct a 90% confidence interval for the mean of the revised test - [14.6 +/- 1.65*2.4/30^.5 -> (13.88, 15.32)]
p. 388 - 1, 3, 5, 11, 13
[I do not cover chapter 9]
[I do chapter 10 after the third test]
p. 589 - 1, 3
p. 575 - 1, 7, 9, 11
[Third test]
p. 481 - 1, 5, 7, 13
p. 490 - 1, 5, 11, 23, 25, 27
p. 515 - 1, 5, 11
p. 537 - 1, 5, 11 [N.B.: $b_{1} \times SS_{xy}/SS_{xx} = (SS_{xy}/\sqrt{SS_{xx}SS_{yy}})^{2}$]
p. 545 - 1a, 5a, 11ac
[Final]