## Related questions with answers

In 1970, 59% of college freshmen thought that capital punishment should be abolished; by 2005, the percentage had dropped to 35%. Is the difference real, or can it be explained by chance? You may assume that the percentages are based on two independent simple random samples, each of size 1,000.

Solution

VerifiedGiven:

$\begin{align*} \text{Percentage A}&=59\% \\ \text{Percentage B}&=35\% \\ \text{Sample size A}&=1000 \\ \text{Sample size B}&=1000 \end{align*}$

The box corresponding to the 1970 data contains a ticket per freshman, where the value on the ticket is a 1 when he/she thinks that capital punishment should be abolished and otherwise the value on the ticket is 0. The box corresponding to the 2005 data contains a ticket per freshman, where the value on the ticket is a 1 when he/she thinks that capital punishment should be abolished and otherwise the value on the ticket is 0.

The null hypothesis states that the two boxes contains have the same percentage, while the alternative hypothesis states that the percentages are different.

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