The Gallup poll asks respondents how they would rate the honesty and ethical standards of people in different fields - very high, high, average, low, or very
low. 22 The percentage who rated clergy "very high or high" dropped from
60$\%$ in 2000 to 54$\%$ in $2005 .$ This may have been due to scandals involving
sex abuse; or it may have been a chance variation. (You may assume that in
each year, the results are based on independent simple random samples of
$1,000$ persons in each year.)
(a) Should you make a one-sample z -test or a two-sample z -test? Why?
(b) Formulate the null and alternative hypotheses in terms of a box model.
Do you need one box or two? Why? How many tickets go into each
box? How many draws? What do the tickets show? What do the null
and alternative hypotheses say about the box(es)?
(c) Can the difference between 60%$ and 54%$ be explained as a chance
variation? Or was it the scandals? Or something else?