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The personnel manager of a large corporation is studying punctuality among clerical workers at one of...

The personnel manager of a large corporation is studying punctuality among clerical workers at one of the corporation’s branch offices during the past year. Data has been collected on a random sample of 287 employees. Twenty-one were found to be late on more than 10 days.

Test at the 5% level of significance whether the data indicate that the proportion who were late on more than 10 days is less than 8%.

(a) State, in words and in symbols, the hypotheses being tested.  

(b) What is the p-value?

(c) Is there evidence to reject the null hypothesis? Justify your answer.

(d) State the conclusion in context.

(e) Set up a 95% confidence interval to estimate the proportion of clerical workers who were late on more than 10 days in the previous year. Write a sentence to explain the meaning of your answer.     

(f) Write a sentence comparing answers above to (d) and (e).

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