Are job applicants with easy to pronounce last names just as likely to get called for an interview than applicants with difficult to pronounce last names. 519 job applications were sent out with last names that are easy to pronounce and 793 identical job applications were sent out with names that were difficult to pronounce. 337 of the "applicants" with easy to pronounce names were called for an interview while 557 of the "applicants" with difficult to pronounce names were called for an interview. What can be concluded at the 0.05 level of significance? For this study, we should use Select an answer t-test for a population mean z-test for a population proportion t-test for the difference between two dependent population means z-test for the difference between two population proportions t-test for the difference between two independent population means The null and alternative hypotheses would be: H0:H0: Select an answer p1 μ1 Select an answer < > = ≠ Select an answer μ2 p2 (please enter a decimal) H1:H1: Select an answer μ1 p1 Select an answer < = ≠ > Select an answer p2 μ2 (Please enter a decimal) The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer fail to reject reject accept the null hypothesis. Thus, the final conclusion is that ... The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that among all possible applicants, there is a differnece in the population proportion of callbacks for applicants with easy to pronounce last names and applicants with difficult to pronounce names. The results are statistically insignificant at αα = 0.05, so we can conclude that the population proportion of people with easy to pronounce names who get called for an interview is equal to the population proportion of people with difficult to pronounce names who get called for an interview. The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that among all possible applicants, there is a differnece in the population proportion of callbacks for applicants with easy to pronounce last names and applicants with difficult to pronounce names. The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the proportion of the 519 applicants with easy to pronounce names who got called for an interview is not the same as the proportion of the 793 applicants with difficult to pronounce names who got called for an interview. Interpret the p-value in the context of the study. There is a 4.36% chance of a Type I error. If the population proportion of callbacks for applicants with easy to pronounce last names is the same as the population proportion of callbacks for applicants with difficult to pronounce last names and if another 519 applications with easy to pronounce names and 793 applications with difficult to pronounce names are submitted then there would be a 4.36% chance that the percent of callbacks for the sample of applicants with easy to pronounce names and the percent of callbacks for the sample of applicants with difficult to pronounce names would differ by at least 5.3%. If the sample proportion of applicants with easy to pronounce names who receive a callback is the same as the sample proportion of applicants with difficult to pronounce names who receive a callback and if another another 519 applications with easy to pronounce names and 793 applications with difficult to pronounce names are submitted then there would be a 4.36% chance of concluding that the percent callbacks for applicants with easy to pronounce names and applicants with difficult to pronounce names differ by at least 5.3% . There is a 4.36% chance that percent of callbacks for applicants with easy to pronounce names and those with difficult to pronounce names differ by at least 5.3%.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Are job applicants with easy to pronounce last names just as likely to get called for an interview than applicants with difficult to pronounce last names. 519 job applications were sent out with last names that are easy to pronounce and 793 identical job applications were sent out with names that were difficult to pronounce. 337 of the "applicants" with easy to pronounce names were called for an interview while 557 of the "applicants" with difficult to pronounce names were called for an interview. What can be concluded at the 0.05 level of significance?
For this study, we should use Select an answer t-test for a population mean z-test for a population proportion t-test for the difference between two dependent population means z-test for the difference between two population proportions t-test for the difference between two independent population means
- The null and alternative hypotheses would be:
H0:H0: Select an answer p1 μ1 Select an answer < > = ≠ Select an answer μ2 p2 (please enter a decimal)
H1:H1: Select an answer μ1 p1 Select an answer < = ≠ > Select an answer p2 μ2 (Please enter a decimal)
- The test statistic ? t z = (please show your answer to 3 decimal places.)
- The p-value = (Please show your answer to 4 decimal places.)
- The p-value is ? > ≤ αα
- Based on this, we should Select an answer fail to reject reject accept the null hypothesis.
- Thus, the final conclusion is that ...
- The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that among all possible applicants, there is a differnece in the population proportion of callbacks for applicants with easy to pronounce last names and applicants with difficult to pronounce names.
- The results are statistically insignificant at αα = 0.05, so we can conclude that the population proportion of people with easy to pronounce names who get called for an interview is equal to the population proportion of people with difficult to pronounce names who get called for an interview.
- The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that among all possible applicants, there is a differnece in the population proportion of callbacks for applicants with easy to pronounce last names and applicants with difficult to pronounce names.
- The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the proportion of the 519 applicants with easy to pronounce names who got called for an interview is not the same as the proportion of the 793 applicants with difficult to pronounce names who got called for an interview.
- Interpret the p-value in the context of the study.
- There is a 4.36% chance of a Type I error.
- If the population proportion of callbacks for applicants with easy to pronounce last names is the same as the population proportion of callbacks for applicants with difficult to pronounce last names and if another 519 applications with easy to pronounce names and 793 applications with difficult to pronounce names are submitted then there would be a 4.36% chance that the percent of callbacks for the sample of applicants with easy to pronounce names and the percent of callbacks for the sample of applicants with difficult to pronounce names would differ by at least 5.3%.
- If the sample proportion of applicants with easy to pronounce names who receive a callback is the same as the sample proportion of applicants with difficult to pronounce names who receive a callback and if another another 519 applications with easy to pronounce names and 793 applications with difficult to pronounce names are submitted then there would be a 4.36% chance of concluding that the percent callbacks for applicants with easy to pronounce names and applicants with difficult to pronounce names differ by at least 5.3% .
- There is a 4.36% chance that percent of callbacks for applicants with easy to pronounce names and those with difficult to pronounce names differ by at least 5.3%.
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