# 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

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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 \$29,600.

a. State the appropriate null and alternative hypotheses.
b. Assuming the population standard deviation is known to be \$3,500 and the significance level for the test is to be 0.10, 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.

c. Which of the two statistical errors might have been made in this case? Explain.

A. A Type I error might have been made because the null hypothesis was rejected.
B. A Type II error might have been made because the null hypothesis was not rejected. C. A Type II error might have been made because the null hypothesis was rejected.
D A Typee I error might have been made herause the null hvnothesis was not rejecteed This is a one-tailed test,

so the hypotheses are:  Ho: mu = \$30,000

Ha: mu < \$30,000

The critical value for the left-tailed test can be obtained using the Excel spreadsheet,  =NORM.S.INV(0.1)  = -1.283

The null hypothesis will be rejected if the test statistic is less than the critical value.

Test statistic  = Z = (29600 - 30000)/(3500/sqrt(100))  = -1.14, Do not reject the null hypothesis, the test statistic is not less than the critical value.

Type two error is made when the null hypothesis is not rejected, the Type II error might have been made.