Question

A meterologist who sampled 13 thunderstorms found that the average speed at which they traveled across a certain state was 15 miles per hour. Suppose the distribution is normal and that the population standard deviation is 1.7 miles per hour. A 99% confidence interval of the mean was found to be (13.6, 16.4).

1) If a meteorologist wanted to use the highest speed to predict the times it would take storms to travel across the state in order to issue warnings, what figure would they likely use? Explain your answer.

2) Describe in a complete sentence an appropriate interpretation of this confidence interval.

3) Based on the given confidence interval, what would the margin of error be?

4) If a meteorologist wanted a 99% confidence interval to have a margin of error of 0.5, what sample size would they need? You may use your calculator or statdisk to compute this.

Answer 1

1) He must use 16.4, that is, the upper bound of the 99% confidence interval. Because this is the upper bound to the 99% CI, and the chance of getting a speed beyond this is only .01/2=0.5%.

2) In repeated sampling, the interval (13.6, 16.4) contains the true average speed of thunderstorms 99% times.

3) CI=(sample mean-margin of error,sample mean+margin of error). Thus sample mean-margin of error=13.6 or

margin of error(ME)=15-13.6=1.4.

4) Margin of error=

ME=.5 gives n=76.6994 or n=77(approximated to nearest integer)