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The research showed that $113231$violent crimes in Texas in $2010,7622$of them were forcible rapes. In $2011,7439$of the $104873$violent crimes was in the forcible rape category. Test at $5\%$significant level.

This is a test of two proportions.

The distribution to perform the test is the normal distribution.

The random variable $X$is the number of forcible rapes in Texas every year.

The null hypothesis $H_0$: The proportion of forcible rapes in Texas in $2011and2010$are same.

The alternative hypothesis: $H_a$: The proportion of forcible rapes in Texas in $2011and2010$are different.

The null and alternative hypothesis:

$$\begin{gathered} H_0:p_1=p_2 \\ {H}_a:p_1鈮�p_2 \end{gathered}$$

The test is about the difference in the proportion of forcible rapes, therefore, it is two-tailed. Hence, the test is two-tailed.

The p-value is$0.0693$

Here, $p-value>\text{significantvalue,}$so we do not reject the null hypothesis.

At the $5\%$level of significance, from the sample data, there issufficient evidence to conclude that the proportion of forcible rapes in Texas in $2011and2010$are the same.