# A Company's Average Absentee Rate and P-Value Interpretation

1. Over the last year the absentee rate at a large corporation averaged 8.2 days absent with a standard deviation of 6 days. One department with 40 employees had an absentee rate of 12 days per employee. During an investigation the department head argued as follows: 'If you took 40 employees at random from the corporation, there is a pretty good chance the average number of days absent would be 12 or more. That's what happened to us---chance variation.' Is this a good defense? Justify your answer.

2. Market researchers would like to know if customers prefer a well-known brand over a generic brand of soft drink. They give a large sample of people the two drinks to taste in a random order and ask them which one tastes better. They find that 70% of people say the branded one and researchers compute a p-value of .02. Interpret this number.

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#### Solution Preview

1. Over the last year the absentee rate at a large corporation averaged 8.2 days absent with a standard deviation of 6 days. One department with 40 employees had an absentee rate of 12 days per employee. During an investigation the department head argued as follows: "If you took 40 employees at random from the corporation, there is a pretty good chance the average number of days absent would be 12 or more. That's what happened to us---chance variation." Is this a good defense? Justify your answer.

It's only a good defense if there really is a "pretty good chance" that you could choose a sample of 40 employees with so many absences. We can use z-scores to determine the probability of choosing a sample of 40 people who had 12 absences from a population of people with an average of ...

#### Solution Summary

The response answers the questions in 497 words, backing up all worded explanation with thorough calculations and including 4 references at the end.