A random sample of size 25 was selected from a population and from that sample the value of a statistic,which we will label ,was determined to be = 6.250.Using the bootstrap method,5000 resamples were obtained from the sample observations.The histogram of the values of the statistic from these 5000 resamples looked reasonably Normal.The 5000 's had a mean of 6.234 and standard deviation of 1.493.An approximate 95% confidence interval for the parameter that corresponds to is given by
A)6.234 ± 2.064(0.299).
B)6.234 ± 2.064(1.493).
C)6.250 ± 2.064(1.493).
D)6.250 ± 2.064(0.299).
E)6.250 ± 1.960(1.493).

Question

A random sample of size 25 was selected from a population and from that sample the value of a statistic,which we will label  ,was determined to be  = 6.250.Using the bootstrap method,5000 resamples were obtained from the sample observations.The histogram of the values of the  statistic from these 5000 resamples looked reasonably Normal.The 5000  's had a mean of 6.234 and standard deviation of 1.493.An approximate 95% confidence interval for the parameter that corresponds to  is given by
A)6.234 ± 2.064(0.299). 
B)6.234 ± 2.064(1.493). 
C)6.250 ± 2.064(1.493). 
D)6.250 ± 2.064(0.299). 
E)6.250 ± 1.960(1.493).

Quizplus · Accepted Answer

The confidence interval for the parameter corresponding to the statistic 11eab14b_c879_7d7d_9166_99c7ff6ca9e1_TB5065_11 can be obtained by adding and subtracting 2.064 times the standard deviation of the bootstrap distribution from the sample statistic. Therefore, the confidence interval is given by 6.250 ± 2.064(1.493) which simplifies to 6.250 ± 3.084. The approximate 95% confidence interval is then (6.250 - 3.084, 6.250 + 3.084) = (3.166, 9.334) which contains the true parameter value with 95% probability.

A Random Sample of Size 25 Was Selected from a Population