5. In problem 4, the candidate wants to get a better estimate of her chances, so she commissions another poll, and this time she asks 1000 potential voters, and 510 indicate that they will vote for her. Does this represent a significant drop in support from the previous poll?
In problem 4, we found that the percent of people who supported her was 52.5%. In this poll, 510/1000 = 51%. Is this a significant drop? We compute the z score for the difference in two proportions.
If we look this z-score up in Table A we see that it corresponds to an area of
This would give us a p value of
which would not represent a significant difference.
The apparent loss of support could easily be simply due to sampling errors. If you remember, the 95% confidence interval from problem 4 contained proportions which were less than 50%, so it would not be too surprising if the true proportion were actually 51% in which case this result would be not at all surprising. What the campaign workers would want to do at this point would be to find a 95% confidence interval based on this larger and hence more reliable sample. That is left for the interested student as an exercise.