Questions: Are job applicants with easy to pronounce last names less likely to get called for an interview than applicants with difficult to pronounce last names? 628 job applications were sent out with last names that are easy to pronounce and 884 identical job applications were sent out with names that were difficult to pronounce. 475 of the "applicants" with easy to pronounce names were called for an interview while 694 of the "applicants" with difficult to pronounce names were called for an interview. What can be concluded at the 0.10 level of significance? If the calculator asks, be sure to use the "Not Pooled" data option.

Are job applicants with easy to pronounce last names less likely to get called for an interview than applicants with difficult to pronounce last names? 628 job applications were sent out with last names that are easy to pronounce and 884 identical job applications were sent out with names that were difficult to pronounce. 475 of the "applicants" with easy to pronounce names were called for an interview while 694 of the "applicants" with difficult to pronounce names were called for an interview. What can be concluded at the 0.10 level of significance? If the calculator asks, be sure to use the "Not Pooled" data option.

Transcript text: Are job applicants with easy to pronounce last names less likely to get called for an interview than applicants with difficult to pronounce last names? 628 job applications were sent out with last names that are easy to pronounce and 884 identical job applications were sent out with names that were difficult to pronounce. 475 of the "applicants" with easy to pronounce names were called for an interview while 694 of the "applicants" with difficult to pronounce names were called for an interview. What can be concluded at the 0.10 level of significance? If the calculator asks, be sure to use the "Not Pooled" data option.

Solution

Solution Steps

Step 1: Define the Hypotheses

We set up our hypotheses as follows:

Null Hypothesis (\(H_0\)): \(p_1 = p_2\) (The proportion of applicants with easy to pronounce names who get called for an interview is equal to that of applicants with difficult to pronounce names.)
Alternative Hypothesis (\(H_1\)): \(p_1 < p_2\) (The proportion of applicants with easy to pronounce names who get called for an interview is less than that of applicants with difficult to pronounce names.)

Step 2: Calculate Sample Proportions

We calculate the sample proportions for both groups:

For easy to pronounce names: \[ \hat{p}_1 = \frac{475}{628} \approx 0.7564 \]
For difficult to pronounce names: \[ \hat{p}_2 = \frac{694}{884} \approx 0.7851 \]

Step 3: Calculate the Test Statistic

The test statistic \(Z\) is calculated using the formula: \[ Z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\frac{p_2(1 - p_2)}{n_1}}} \] Substituting the values: \[ Z = \frac{0.7564 - 0.7851}{\sqrt{\frac{0.7851(1 - 0.7851)}{628}}} \approx -1.7508 \]

Step 4: Calculate the P-value

The calculated p-value associated with the test statistic is: \[ \text{P-value} = 0.0400 \]

Step 5: Decision Rule

We compare the p-value with the significance level \(\alpha = 0.10\):

Since \(0.0400 < 0.10\), we reject the null hypothesis.

Final Conclusion

Based on the results, we conclude that there is sufficient evidence to suggest that the proportion of applicants with easy to pronounce last names who get called for an interview is less than that of applicants with difficult to pronounce last names.

Final Answer

\(\boxed{\text{The results are statistically significant at } \alpha=0.10, \text{ so there is sufficient evidence to conclude that the proportion of applicants with easy to pronounce names who got called for an interview is less than that of applicants with difficult to pronounce names.}}\)

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!