Advertisements for the Sylph Physical Fitness Center claim that completion of their course will result in a loss of weight (meas
ured in pounds). A random sample of 8 recent students revealed the following body weights before and after completion of SPF course. Student 1 2 3 4 5 6 7 8
Before 155 228 141 162 211 185 164 172
After 154 207 147 157 196 180 150 165
The above data summarizes to the following (Note that "Difference = Before - After").
Mean Std Dev
Before 177.25 29.325
After 169.50 22.431
Difference 7.75 8.598
Construct a 90% confidence interval for the mean weight loss for the population represented by this sample assuming that the differences are coming from a normally distributed population.
90% confidence interval for the mean weight loss for the population represented by this sample assuming that the differences are coming from a normally distributed population is [1.989 ,13.5105]
Step-by-step explanation:
The data given is
Mean Std Dev
Before 177.25 29.325
After 169.50 22.431
Difference 7.75 8.598
Hence d`= 7.75 and sd= 8.598
The 90% confidence interval for the difference in means for the paired observation is given by
d` ± t∝/2(n-1) *sd/√n
Here t∝/2(n-1)=1.895 where n-1= 8-1= 7 d.f
and ∝/2= 0.1/2=0.05
Putting the values
d` ± t∝/2(n-1) *sd/√n
7.75 ±1.895 * 8.598 /√8
7.75 ± 5.7605
1.989 ,13.5105
90% confidence interval for the mean weight loss for the population represented by this sample assuming that the differences are coming from a normally distributed population is [1.989 ,13.5105]
