Index

A

  • addition rule, 237–239, 251–252
  • alternative hypothesis (Ha), 178
  • anecdotes, 307
  • average. See mean
  • average, of histograms, 47

B

  • bar graphs (bar charts), 32–36, 40–42
  • bell curve. See normal distribution
  • bell-shaped histograms, 47
  • bias, 65, 146, 225, 302–303
  • bimodal histograms, 47
  • binomial distribution, 105–116
    • binomial table, 314–318
    • mean and variance of, 110–111, 115–116
    • overview, 105–106, 114
    • probabilities for large sample cases (normal approximation), 112–113, 116
    • probabilities for medium sample cases, 109–110, 115
    • probabilities for small sample cases, 107–108, 114–115
  • binomial table, 314–318
  • box plots, 55–57, 67–68

C

  • categorical data, 7–15
    • bar graphs, 32–36, 40–42
    • counts and percents, 11–12, 15
    • frequency, 7–9, 13–14
    • independence of variables, 246–249, 255–257
    • percentages, 9–11, 14–15
    • pie charts, 27–32, 37–40
  • center, measures of, 18–20, 24–25
  • central limit theorem (CLT), 126–128
    • finding probabilities with, 129–130, 134–135
    • overview, 128, 133–134
  • coefficient of variation, 65
  • complex fractions, 281
  • conditional probabilities
    • key words for, 242
    • two-way tables, 242–245, 252–255
  • confidence intervals, 151–162, 169–174
    • components of, 151
    • for difference of two means, 158–160, 165–166
    • for difference of two proportions, 160–162, 166–167
    • evaluating, 173–174, 176
    • interpreting, 169–173, 175–176
    • overview, 151–154, 163
    • for population mean, 154–156, 163–164
    • for population proportion, 156–158, 164
    • steps for calculating, 152
  • confounding variables, 225, 230, 305
  • correlation, 284–285
    • avoiding mistakes with, 305
    • calculating, 262–264, 272
    • defined, 292
    • formula for, 292–293
    • properties of, 262
  • crosstabs. See two-way tables

D

  • data snooping (data fishing), 306–307
  • degrees of freedom, 118, 120–122
  • denominators, 280
  • disjoint outcomes, 76
  • double-blind experiments, 226, 231

E

  • empirical rule (68-95-99.7 rule), 60–62, 69–71
  • experiments, 223–231
    • confounding variables and, 305
    • defined, 223
    • designing, 225–228, 230–231
    • interpreting results, 228–229, 231
    • observational studies vs., 223–225, 230
  • extrapolation, 268

F

  • five number summary, 55
  • formulas, 283–299
    • correlation, 292–293
    • handling complicated, 283–285
    • margin of error for the sample mean, 293–294
    • margin of error for the sample proportion, 296–297
    • mean, 289–290
    • median, 290–291
    • overview, 283
    • sample size for estimating μ, 294–295
    • sample size for estimating p, 297–298
    • standard deviation, 291–292
    • test statistic for the mean, 295–296
    • test statistic for the proportion, 298–299
  • fractions, 280–281, 286
    • complex, 281
    • denominators, 280
    • numerators, 280
    • parentheses in, 281
  • frequency and frequency tables, 27
    • interpreting counts and percents, 11–12, 15
    • overview, 7–9, 13–14
  • frequency histograms, 44
  • functions, 285

G

  • grand totals, 234

H

  • Ha (alternative hypothesis), 178
  • histograms, 44–54
    • avoiding mistakes with, 302
    • creating, 44–46, 63–64
    • overview, 47–51, 64–65
    • recognizing misleading, 53–54, 66–67
    • skewed data in, 51–53, 66
  • Ho (null hypothesis), 177–178
  • hypothesis tests, 177–191
    • alternative hypothesis (Ha), 178
    • converting sample statistic to test statistic, 178
    • critical values, 178–179
    • defined, 177
    • for difference between two population means, 185–187, 194–195
    • for mean difference, 188–189, 195–196
    • null hypothesis (Ho), 177–178
    • overview, 180–181, 192
    • for population mean, 181–183, 193
    • for population proportion, 183–185, 194
    • rejection region and nonrejection region, 179
    • for two population proportions, 190–191, 196

I

  • independence of categorical variables, 246–249, 255–257
  • interquartile range (IQR), 22–23, 25
  • intersection probability, 237–239, 251–252

K

  • kth percentile, 22, 88

L

  • left skewed histograms, 47
  • line graphs (time charts), 58–60, 68–69, 302
  • linear functions, 285

M

  • margin of error, 139–147
    • avoiding mistakes with, 303
    • components of, 140
    • defined, 139
    • increasing and decreasing, 144–145, 149–150
    • interpreting, 146–147, 150
    • for means and proportions, 142–144, 148–149, 293–294, 296–297
    • overview, 139–141, 148
  • marginal probabilities, 240–241, 253
  • marginal totals, 234
  • math symbols, 279–280
  • mean (average)
    • calculating in binomial distribution, 110–111, 115–116
    • defined, 18
    • formula for, 289–290
    • notation for, 289
    • skewed data and, 24
  • median
    • defined, 18
    • formula for, 290–291
    • histograms, 47
  • Microsoft Excel, 37–38
  • Minitab statistical software, 37, 44
  • mound-shaped data sets, 60
  • multiplication rule, 243–245, 253–255

N

  • negative linear relationship, 260
  • normal approximation, 112–113, 116
  • normal distribution (bell curve), 83–103
    • overview, 83–85, 95–97
    • percentiles, 88–90, 99–100
    • percentiles (backwards normal), 92–94, 102–103
    • probabilities, 90–92, 100–102
    • standard scores (Z-scores), 86–88, 97–99
  • null hypothesis (Ho), 177–178
  • numerators, 280

O

  • observational studies
    • confounding variables and, 305
    • defined, 223
    • experiments vs., 223–225, 230
  • order of operations, 281–282
  • outliers, 17, 20
    • effect on mean, 290
    • effect on median, 291
    • effect on standard deviation, 292
    • sensational stories as, 307

P

  • paired t-tests, 188–189
  • parentheses, 281
  • PEMDAS, 281
  • percentage returns, 65
  • percentages
    • interpreting, 11–12, 15
    • summarizing categorical data, 9–11, 14–15
  • percentiles
    • backwards normal, 92–94, 102–103
    • calculating from normal distribution, 88–90, 99–100
    • kth percentile, 22
    • in quantitative data, 22–23, 25
  • pie charts
    • avoiding mistakes with, 301
    • common problems with, 28
    • organizing categorical data, 27–32, 37–40
  • placebo effect, 231
  • plus or minus sign (±), 279
  • polls. See surveys
  • positive linear relationship, 260
  • powers, 280
  • predictions
    • probability, 79–80, 82
    • regression lines, 267–269, 274–275
  • probabilities, 75–82
    • central limit theorem, 129–130, 134–135
    • medium sample cases, 109–110, 115
    • misconceptions about, 78–79, 81–82
    • normal distribution, 90–92, 100–102
    • predictions, 79–80, 82
    • rules of, 75–77, 81
    • small sample cases, 107–108, 114–115
  • p-values, 197–203

Q

  • quantitative data, 17–25, 43–71, 259–276
    • box plots, 55–57, 67–68
    • correlation, 262–264, 272
    • empirical rule, 60–62, 69–71
    • histograms, 44–54, 63–67
    • interquartile range, 22–23, 25
    • line graphs, 58–60, 68–69
    • measures of center, 18–20, 24–25
    • measures of spread, 20–22, 25
    • percentiles, 22–23, 25
    • regression lines, 265–276
    • scatterplots, 259–261, 272

R

  • random samples
    • avoiding mistakes with, 304
    • selecting for surveys, 215–217, 220–221
  • range, 20, 47
  • regression lines, 265–276
    • checking fit of, 269–271, 275–276
    • formula for, 265
    • picking out best fitting, 265–267, 272–274
    • predictions, 267–269, 274–275
  • relative frequency, 9–10, 44
  • response bias, 65
  • response rate, 306
  • right skewed histograms, 47
  • right-tail probabilities, 120, 312–313
  • rounding off numbers, 282–283
  • row count, 240

S

  • saddle points, 84
  • sample size
    • anecdotes and, 307
    • avoiding mistakes with, 303–304
    • formulas, 294–295, 297–298
  • sample space, 76
  • sampled population, 215
  • sampling distributions, 123–136
    • central limit theorem, 126–130, 133–135
    • properties of, 124–126, 133
    • t-distribution, 131–132, 135–136
  • scale distortion, 302
  • scatterplots, 259–261, 272
  • 68-95-99.7 rule (empirical rule), 60–62, 69–71
  • skewed data, 22, 51–53, 66
  • slope, 265, 285
  • spread
    • histograms, 47
    • measures of, 20–22, 25
  • square roots, 280
  • standard deviation, 20, 291–292
    • calculating, 21
    • formula for, 291–292
    • histograms, 47
  • standard error, 124
  • standard normal distribution (Z-distribution), 86, 309–311
  • standard scores (Z-scores), 86–88, 97–99
  • statistical model, 267
  • summation sign, 279
  • surveys, 213–222
    • carrying out, 217–218, 221
    • interpreting and evaluating results, 218–219, 221–222
    • planning and designing, 214–215, 220
    • random samples, 215–217, 220–221
    • steps for, 213
  • symmetric histograms, 47

T

  • target population, 215
  • t-distribution, 117–122
    • degrees of freedom, 120–122
    • overview, 117–119, 122
    • small sampling distribution, 131–132, 135–136
    • t-tables, 120–122, 312–313
  • test statistic
    • calculating for proportion, 298–299
    • calculating for sample mean, 295–296
  • time charts (line graphs), 58–60, 68–69, 302
  • total sample size, 27
  • t-tables, 120–122, 312–313
  • t-tests, 181–182
  • two-sided hypothesis test, 295
  • two-way tables (crosstabs), 233–257
    • addition rule, 237–239, 251–252
    • conditional probabilities, 242–245, 253–255
    • independence of categorical variables, 246–249, 255–257
    • intersection probability, 237–239, 251–252
    • marginal probabilities, 240–241, 253
    • multiplication rule, 243–245, 253–255
    • overview, 234–236, 250–251
    • union probability, 237–239, 251–252
  • Type I errors, 204–205, 209
  • Type II errors, 205–207, 209–210

U

  • uniform histograms, 47
  • union probability, 237–239, 251–252
  • U-shaped histograms, 47

V

Z

  • Z* values, 140, 151–152
  • Z-distribution (standard normal distribution), 86, 309–311
  • Z-scores (standard scores), 86–88, 97–99
  • Z-tables, 88, 90, 309–311
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