Question: An organisation wants to find out how a batch of new job applicants compare with applicants in the past on a performance test. Historically, the average score on the test has been 475 points. The test scores from a sample of 80 new applicants are analysed. Based on hypothesis testing, the following decision rule is defined to answer the question:

If the average score for the new applicant batch is less than 453 or greater than 497 then conclude that the new batch of applicants is significantly different from historical norms.

1. State the null and alternate hypotheses
2. If the sample mean is 510 points, how would you apply the decision rule and what would you conclude?
3. If the sample yields a standard deviation of 100 points, what is the α level of the test that has been employed?
4. If you set the decision points at 440 and 510 instead of 453 and 497, by how many standard errors has the hypothesized population mean been "stretched" on either side?

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