(C) Referring to your answer in part b, what conclusion should be reached with respect to the null hypothesis?

College Algebra (MindTap Course List)
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ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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5. The director of a state agency believes that the average starting salary for clerical employees in
the state is less than $30,000 per year. To test her hypothesis, she has collected a simple random
sample of 100 starting clerical salaries from across the state and found that the sample mean is
$29,750.
(A) State the appropriate null and alternative hypotheses.
(B) Assuming the population standard deviation is known to be $2,500 and the significance level for
the test is to be 0.025, what is the critical value (stated in dollars)?
(C) Referring to your answer in part b, what conclusion should be reached with respect to the null
hypothesis?
(D) Referring to your answer in part c, which of the two statistical errors might have been made in this
case? Explain.
Transcribed Image Text:5. The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,000 per year. To test her hypothesis, she has collected a simple random sample of 100 starting clerical salaries from across the state and found that the sample mean is $29,750. (A) State the appropriate null and alternative hypotheses. (B) Assuming the population standard deviation is known to be $2,500 and the significance level for the test is to be 0.025, what is the critical value (stated in dollars)? (C) Referring to your answer in part b, what conclusion should be reached with respect to the null hypothesis? (D) Referring to your answer in part c, which of the two statistical errors might have been made in this case? Explain.
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