In: Statistics and Probability
The weights (in pounds) of 30 participants are recorded before and after a 6 week exercise program.
Before | After |
---|---|
210 | 207 |
174 | 176 |
150 | 148 |
124 | 130 |
222 | 220 |
287 | 280 |
175 | 168 |
173 | 170 |
264 | 255 |
247 | 250 |
Before | After |
---|---|
185 | 184 |
134 | 135 |
157 | 155 |
245 | 242 |
255 | 247 |
148 | 150 |
170 | 165 |
215 | 210 |
309 | 300 |
234 | 230 |
Before | After |
---|---|
245 | 240 |
287 | 276 |
200 | 201 |
186 | 184 |
310 | 308 |
167 | 165 |
190 | 185 |
220 | 215 |
275 | 270 |
225 | 22 |
Question - Part 1
Calculate the difference between the before weight and after weight of all 30 participants, where a negative value represents losing weight. Then, find the mean difference of weights. (Round your answer to the nearest hundredth)
Question - Part 2
Next, find the sample standard deviation for the difference of weights. (Round your answer to the nearest hundredth)
Question - Part 3
The goal is to find the 90% confidence interval for the difference in weight. Find the t-critical value. (Round your answer to the nearest thousandth)
t.9 = ____
Question Part 4
Find the error, E, for the 90% confidence interval. (Round your answer to the nearest hundredth)
E = ____
Question - Part 4
Find the 90% confidence interval for the difference in weights. (Round all answers to the nearest hundredth)
< d <
before after d= before-after d-dbar (d-dbar)^2
210 | 207 | 3 | -0.233 | 0.054289 |
174 | 176 | -2 | -5.233 | 27.38429 |
150 | 148 | 2 | -1.233 | 1.520289 |
124 | 130 | -6 | -9.233 | 85.24829 |
222 | 220 | 2 | -1.233 | 1.520289 |
287 | 280 | 7 | 3.767 | 14.19029 |
175 | 168 | 7 | 3.767 | 14.19029 |
173 | 170 | 3 | -0.233 | 0.054289 |
264 | 255 | 9 | 5.767 | 33.25829 |
247 | 250 | -3 | -6.233 | 38.85029 |
185 | 184 | 1 | -2.233 | 4.986289 |
134 | 135 | -1 | -4.233 | 17.91829 |
157 | 155 | 2 | -1.233 | 1.520289 |
245 | 242 | 3 | -0.233 | 0.054289 |
255 | 247 | 8 | 4.767 | 22.72429 |
148 | 150 | -2 | -5.233 | 27.38429 |
170 | 165 | 5 | 1.767 | 3.122289 |
215 | 210 | 5 | 1.767 | 3.122289 |
309 | 300 | 9 | 5.767 | 33.25829 |
234 | 230 | 4 | 0.767 | 0.588289 |
245 | 240 | 5 | 1.767 | 3.122289 |
287 | 276 | 11 | 7.767 | 60.32629 |
200 | 201 | -1 | -4.233 | 17.91829 |
186 | 184 | 2 | -1.233 | 1.520289 |
310 | 308 | 2 | -1.233 | 1.520289 |
167 | 165 | 2 | -1.233 | 1.520289 |
190 | 185 | 5 | 1.767 | 3.122289 |
220 | 215 | 5 | 1.767 | 3.122289 |
275 | 270 | 5 | 1.767 | 3.122289 |
225 | 220 | 5 | 1.767 | 3.122289 |
mean difference of weights,
sample standard deviation for difference of weights ,
df = 30-2= 28
t.9 = 1.7011
E = 1.7011* 3.7831/
= 1.216
90% confidence interval
= 2.01<d<4.44