Chapter PVI, Problem 3RE

To determine

To explain should the firm conclude that its area is unusual and test an appropriate hypothesis and state your conclusion.

Answer to Problem 3RE

There is no sufficient evidence to support the claim that its area is unusual.

Explanation of Solution

It is given in the question that the U.S. census bureau reports that $26\%$ of all U.S. businesses are owned by women. Thus, to find out any test for proportion we will use the calculator $\text{TI}-89$ . Then select $5:1-$ PropZTest from the STAT TESTSmenu. Specify the hypothesized proportion. Enter the observed value of x . Specify the sample size. Indicate what kind of test you want: one-tail lower tail, two-tail, or one-tail upper tail. Specify whether to calculate the result or draw the result. Now let us define the hypothesis as:

The null hypothesis states that the population proportion is equal to the value mentioned in the claim and the alternative hypothesis states the opposite. So,

  $\begin{array}{l}{H}_0:p_1=0.26\\ H_a:p_1\ne 0.26\end{array}$

And we have,

  $\begin{array}{l}x=410\\ n=115\\ \alpha =0.05\end{array}$

Thus, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}P=0.3422\\ z=0.95\end{array}$

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

  $P>0.05\Rightarrow \text{Fail to Reject }{H}_0$

Thus, we conclude that there is no sufficient evidence to support the claim that its area is unusual.