In a survey of 446 students, respondents 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 could be chosen less often than others. Using software to access the survey data, report the sample proportion who picked the number you suspected would be chosen less often.
c. Is the sample proportion in fact lower 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 your 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. Use software to carry out a hypothesis test to see if the sample proportion choosing your number was low enough to assert that, overall, students picked that number less than if they were choosing at random from twenty numbers: Report the standardized sample proportion z.
g. Report the P-value for your test.
h. State your conclusions, using 0.05 as the cutoff for small P-values.