$9$ In an experiment to see if reaction times were affected by whether or not

individuals are hungry, $2000$ randomly chosen soldiers were tested before

and after they had eaten a substantial lunch. The test used was to drop a

metre rule, which was held vertically so that its lower end was level with

the thumb and first finger of each person, and to measure how far the rule

fell before it was caught. For each person, the difference, $d,$ of the distance

measured after lunch minus the distance measured before lunch was found.

From these it was calculated that $d=1626$ and $d^2=258632.$

Use these data to provide a $98\%$ confidence interval for the population mean

difference, stating any assumptions you have made.

What does your confidence interval suggest about reaction times before and

after a meal?