Question

# A researcher computed 90%, 95%, 98% and 99% confidence intervals for a population mean. However, he...

A researcher computed 90%, 95%, 98% and 99% confidence intervals for a population mean. However, he forgot to record which interval was which, and he cannot find the sample data to allow him to recreate the intervals from scratch. He now needs only the 99% confidence interval. Which one is it?

a-(37.9, 42.1)

b-(38.4, 41.6)

c-(38.1, 41.9)

d-(38.7, 41.3)

As the level of confidence increases, The width of confidence interval increases.

Therefore, Width of 99% confidence interval > (greater than) Width of 98% confidence interval > (greater than) Width of 95% confidence interval > (greater than) Width of 90% confidence interval.

 a-(37.9, 42.1) 42.1-37.9 = 4.2 Highest width, Hence 99% confidnece interval b-(38.4, 41.6) 41.6-38.4 = 3.2 Width is lower than 98% confidence interval c-(38.1, 41.9) 41.9-38.1 = 3.8 Width is lower than 99% confidence interval d-(38.7, 41.3) 41.3-38.7 = 2.6 Width is lower than 95% confidence interval