In: Statistics and Probability
Consider the data below:
302.0207, 306.9998, 300.8687, 270.4524, 259.5252, 288.0257,
283.3269, 294.9006, 292.8622, 322.8245, 329.5085, 313.5145,
307.6594, 325.7587, 354.1881, 324.6396, 276.2345, 283.0315,
278.8270, 298.1269
a. What is your BOOTSTRAP estimate of the mean and standard error
of the
mean? boot:_____ μboot:_____
b. What is your two-sided 95% BOOTSTRAP CI for the
mean? loboot:_____ hiboot:_____
c. What is your one-sided lower 99% BOOTSTRAP CI for the mean? ?
loboot:_____
d. What is your one-sided upper 62% BOOTSTRAP CI for the mean?
hiboot:_____
a)
sample std dev , s = √(Σ(X- x̅ )²/(n-1) )
= 23.1688
Sample Size , n = 20
Sample Mean, x̅ = ΣX/n =
300.6648
degree of freedom= DF=n-1= 19
Standard Error , SE = s/√n = 23.1688 / √
20 = 5.1807
b)
Level of Significance , α =
0.05
degree of freedom= DF=n-1= 19
't value=' tα/2= 2.0930 [Excel
formula =t.inv(α/2,df) ]
Standard Error , SE = s/√n = 23.1688 /
√ 20 = 5.180712
margin of error , E=t*SE = 2.0930
* 5.18071 = 10.843356
confidence interval is
Interval Lower Limit = x̅ - E = 300.66
- 10.843356 = 289.821414
Interval Upper Limit = x̅ + E = 300.66
- 10.843356 = 311.508126
95% confidence interval is (
289.82 < µ < 311.51 )
c)
Level of Significance , α =
0.01
degree of freedom= DF=n-1= 19
't value=' tα/2= 2.8609 [Excel
formula =t.inv(α/2,df) ]
Standard Error , SE = s/√n = 23.1688 /
√ 20 = 5.180712
margin of error , E=t*SE = 2.8609
* 5.18071 = 14.821679
confidence interval is
Interval Lower Limit = x̅ - E = 300.66
- 14.821679 = 285.843091
d)
Level of Significance , α =
0.38
degree of freedom= DF=n-1= 19
't value=' tα/2= 0.8988 [Excel
formula =t.inv(α/2,df) ]
Standard Error , SE = s/√n = 23.1688 /
√ 20 = 5.180712
margin of error , E=t*SE = 0.8988
* 5.18071 = 4.656514
confidence interval is
Interval Upper Limit = x̅ + E = 300.66
- 4.656514 = 305.321284
------------------------------------
DEAR STUDENT,
IF YOU HAVE ANY QUERY ASK ME IN THE COMMENT BOX,I AM HERE TO HELPS YOU.PLEASE GIVE ME POSITIVE RATINGS
*****************THANK YOU***************