Question

1. Let z_0.10, t_{0.10, 5}, and t_{0.10, 20} denote the upper 0.10 quantile (upper 10^thpercentile) of the z-distribution, t-distribution with 5 df, and t-distribution with 20 df, respectively. Sort these values from the smallest to the largest.

Group of answer choices

t_{0.10, 5} < t_{0.10, 20} < z_0.10

t_{0.10, 20} < t_{0.10, 5} < z_0.10

z_0.10 < t_{0.10, 5} < t_{0.01, 20}

z_0.10 < t_{0.10, 20} < t_{0.01, 5}

Based on a random sample, the 68% confidence interval for the population proportion p is (0.46, 0.54). Using the same sample, what would the 99.7% confidence interval for p be? Choose the closest answer.

Group of answer choices

(0.44, 0.56)

(0.42, 0.58)

(0.38, 0.62)

(0.34, 0.66)

Answer 1

1)correct sequence is :

z_0.10 < t_{0.10, 20} < t_{0.01, 5}

₂₎

since margin of error =(UCL-LCL)/2 =(0.54-0.46)/2= 0.04

and point estimate =(UCL+LCL)/2 =(0.54+0.46)/2=0.50

for 99.7% confidence interval margin of error is 3 times that of 68% confidence interval

99.7% confidence interval = 0.5 -/+ 3*0.04 =0.38 ,0.62

(0.38, 0.62)