Determine the null and alternative hypothesis regarding gender discrimination in hiring at Old West Credit Company: After being rejected for employment, Isabel learns that the Old West Credit Company has hired only 5 women among the last 25 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women. She wants to address the claim that the proportion of females hired is less than $50 \%$. Using the sample data stated above: a. The null and alternative hypothesis would be: \[ H_{0}: p \text { Select an answer } \hat{\approx} H_{A}: p \text { Select an answer } \hat{\imath} \] b. The p-value is: $\square$ (to 4 decimals) Because this is a serious claim, we will use a stricter cutoff value for unusual events. We will use $1 \%$ as the cutoff value ( 1 in 100 chance of happening by chance). a. Based on this we: Reject the null hypothesis Fail to reject the null hypothesis With this significance level of $1 \%$ in mind, does the resulting $\mathrm{p}$-value really support a charge of gender discrimination? Isabel does have signifigant evidence to conclude that fewer women have been hired. Isabel do not have signifigant evidence to conclude that fewer women have been hired.

Step 1 ：Formulate the null and alternative hypothesis. The null hypothesis is typically a statement of no effect or no difference. In this case, it would be that the proportion of females hired is equal to 50%. The alternative hypothesis is what we are testing against the null hypothesis. In this case, it would be that the proportion of females hired is less than 50%.

Step 2 ：The null and alternative hypothesis would be: \(H_{0}: p = 0.5\) and \(H_{A}: p < 0.5\)

Step 3 ：Calculate the p-value. The p-value is the probability of obtaining the observed data (or data more extreme) if the null hypothesis is true. We can use the binomial test for this, which tests the null hypothesis that the probability of success on a single trial is a specified value (0.5 in this case). The test statistic is the number of successes (5 women hired) out of the number of trials (25 new employees).

Step 4 ：The p-value is approximately 0.002, which is less than the significance level of 0.01. Therefore, we reject the null hypothesis.

Step 5 ：Interpret the p-value in the context of the problem. If the p-value is less than the significance level, it means that the observed data is unlikely to have occurred by chance if the null hypothesis is true, which would support a charge of gender discrimination.

Step 6 ：The final answer is: The null and alternative hypothesis are: \(H_{0}: p = 0.5\) and \(H_{A}: p < 0.5\). The p-value is approximately \(\boxed{0.002}\). Based on this, we reject the null hypothesis. With a significance level of 1% in mind, the resulting p-value does support a charge of gender discrimination. Therefore, Isabel does have significant evidence to conclude that fewer women have been hired.