Question

13. Percentiles of a bootstrap distribution (based on 5000 samples) are provided. 0.5% 1% 2.5% 5% 95% 97.5% 99% 99.5% -0.945 -0.940 -0.928 -0.919 -0.741 -0.723 -0.705 -0.689 Use the percentiles to provide a 99% confidence interval for the parameter. Indicate the percentiles that you use. Use the percentiles to provide a 98% confidence interval for the parameter. Indicate the percentiles that you use. Use the percentiles to provide a 95% confidence interval for the parameter. Indicate the percentiles that you use.

Answer 1

a)

99% confidence interval for the parameter.

We have to find a and b such that

p(a<Z<b)=0.99

that means p(Z<a) = p(Z>b)=(1-0.99)/2=0.01/2= 0.005 =0.5%

a= -0.945

b such that p(Z<b)=1-0.005 = 0.995 =99.5%

b= -0.689

99% confidence interval for the parameter. = (-0.945 , -0.689 ) =( 0.5% percentile ,99.5% percentile)

b)

98% confidence interval for the parameter.

We have to find a and b such that

p(a<Z<b)=0.98

that means p(Z<a) = p(Z>b)=(1-0.98)/2=0.02/2= 0.01 =1%

a= -0.940

b such that p(Z<b)=1-0.01 = 0.99 =99%

b= -0.705

98% confidence interval for the parameter. = (-0.940 , -0.705 ) =( 1% percentile ,99% percentile)

c)

95% confidence interval for the parameter.

We have to find a and b such that

p(a<Z<b)=0.95

that means p(Z<a) = p(Z>b)=(1-0.95)/2=0.05/2= 0.025 =2.5%

a= -0.928

b such that p(Z<b)=1-0.025 = 0.975 =97.5%

b= -0.723

95% confidence interval for the parameter. = (-0.928 , -0.723) =( 2.5% percentile ,97.5% percentile)

Answer:

99% confidence interval for the parameter. = (-0.945 , -0.689 ) =( 0.5% percentile ,99.5% percentile)

98% confidence interval for the parameter. = (-0.940 , -0.705 ) =( 1% percentile ,99% percentile)

95% confidence interval for the parameter. = (-0.928 , -0.723) =( 2.5% percentile ,97.5% percentile)