Question

In: Statistics and Probability

The weights (in pounds) of 30 participants are recorded before and after a 6 week exercise...

The weights (in pounds) of 30 participants are recorded before and after a 6 week exercise program.

Before and After Weights
Before After
210 207
174 176
150 148
124 130
222 220
287 280
175 168
173 170
264 255
247 250
Before and After Weights
Before After
185 184
134 135
157 155
245 242
255 247
148 150
170 165
215 210
309 300
234 230
Before and After Weights
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 <

Solutions

Expert Solution

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

orchestra answered 3 years ago
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