Suppose a government organization reported the accompanying data on the number of speed-related crash fatalities during holiday periods for the years from 1994 to 2003. Speed-Related Fatalities Holiday Period 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 New Year's Day 143 144 176 76 219 138 171 134 210 70 Memorial Day 195 176 185 197 138 183 156 190 188 181 July 4th 178 219 202 179 169 178 219 64 234 184 Labor Day 189 188 166 179 162 171 180 138 202 189 Thanksgiving 212 198 218 210 203 168 187 217 210 202 Christmas 152 129 66 183 134 191 155 210 60 198 (a) Calculate the standard deviation for the New Year's Day data. (Round the answer to three decimal places.) (b) Without calculating the standard deviation of the Memorial Day data, determine whether the standard deviation for the Memorial Day data would be larger or smaller than the standard deviation of the New Year's Day data. larger smaller (c) Memorial Day and Labor Day are holidays that always occur on Monday and Thanksgiving always occurs on a Thursday, whereas New Year's Day, July 4th, and Christmas do not always fall on the same day of the week every year. Based on the given data, is there more or less variability in the speed-related crash fatality numbers from year to year for same day of the week holiday periods than for holidays that can occur on different days of the week? Support your answer with appropriate measures of variability. (Round your answers to three decimal places.) The standard deviations for Memorial Day, Labor Day, and Thanksgiving are , , and , respectively. The standard deviations for New Year's Day, July 4th, and Christmas are , , and , respectively. The standard deviations for the same day of the week holidays are all than all of the standard deviations for the holidays that can occur on different days of the week. There is variability for the holidays that always occur on the same day of the week.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Suppose a government organization reported the accompanying data on the number of speed-related crash fatalities during holiday periods for the years from 1994 to 2003.
Speed-Related Fatalities
Holiday Period
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
New Year's Day
143
144
176
76
219
138
171
134
210
70
Memorial Day
195
176
185
197
138
183
156
190
188
181
July 4th
178
219
202
179
169
178
219
64
234
184
Labor Day
189
188
166
179
162
171
180
138
202
189
Thanksgiving
212
198
218
210
203
168
187
217
210
202
Christmas
152
129
66
183
134
191
155
210
60
198
(a)
Calculate the standard deviation for the New Year's Day data. (Round the answer to three decimal places.)
(b)
Without calculating the standard deviation of the Memorial Day data, determine whether the standard deviation for the Memorial Day data would be larger or smaller than the standard deviation of the New Year's Day data.
larger
smaller
(c)
Memorial Day and Labor Day are holidays that always occur on Monday and Thanksgiving always occurs on a Thursday, whereas New Year's Day, July 4th, and Christmas do not always fall on the same day of the week every year. Based on the given data, is there more or less variability in the speed-related crash fatality numbers from year to year for same day of the week holiday periods than for holidays that can occur on different days of the week? Support your answer with appropriate measures of variability. (Round your answers to three decimal places.)
The standard deviations for Memorial Day, Labor Day, and Thanksgiving are , , and , respectively. The standard deviations for New Year's Day, July 4th, and Christmas are , , and , respectively. The standard deviations for the same day of the week holidays are all than all of the standard deviations for the holidays that can occur on different days of the week. There is variability for the holidays that always occur on the same day of the week.
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