Question

5. A researcher found a random sample of 35 individuals and recorded the time it took to complete a task. He wished to estimate the mean time it took adults to complete this task. After creating a bootstrap distribution, the following percentiles of the bootstrap distribution are were found and are provided below. Use the percentiles to report a 95% confidence interval for the population parameter. 1% 2.5% 5% 10% 25% 50% 75% 90% 95% 97.5% 99% 6.174 6.322 6.438 6.593 6.866 7.17 7.481 7.78 7.947 8.082 8.304 (6.322 seconds, 8.082 seconds)

Please provide the steps.

Answer 1

Answer

we have to find 95% confidence interval

we know that for confidence interval or two tails, alpha is half of the one tailed alpha value

95% confidence level = 0.05 alpha level (because alpha = 1- confidence level = 1-0.95 = 0.05)

for two sides or confidence interval, we have one lower tail or lower limit and one upper tail

alpha level for lower tail = alpha/2 = 0.05/2 = 0.025

So, lower percentile value for 95% confidence interval is 2.5th percentile value, i.e. 6.322

similarly, alpha level for upper side = confidence level + alpha/2

= 0.95+0.025

= 0.975 or 97.5th percentile

= 8.082

So, confidence interval = (6.322,8.082)