In a survey, 446 students were asked to pick a whole number at random, anywhere from 1 to 20.

a. If all 20 numbers were equally likely to be chosen, what proportion of students would choose each number?

b. Pick a number that you suspect would be chosen more often than others. Using software to access the survey data, report the sample proportion who picked the number you suspected would be chosen more often.

c. Tell whether or not the sample proportion you found in part (b) is in fact higher than the proportion you calculated in part (a).

d. Use software to produce a 95% confidence interval for the proportion of all students who would choose that number. (Report the interval to three decimal places.)

e. Does your confidence interval contain the proportion you calculated in part (a), or is it strictly above, or strictly below?

f. Tell whether a 99% confidence interval would be wider or narrower than the interval you produced in part (d).