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
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
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
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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