Advanced Statistics

2. Test the claim that for the adult population of one town, the mean annual salary is given by μ = 30,000. Sample data are summarized as n = 17, = $22,298, and s = $14,200. Use a significance level of α = 0.05. State the null and alternative hypotheses.

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3. (Refer to Question 2) Find the test statistic.

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4. (Refer to Question 2) Find the critical value(s) and state and explain decision about null hypothesis.

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5. (Refer to Question 2) State the conclusion in non-technical terms.

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6. A manufacturer uses a new production method to produce steel rods. A random sample of 17 steel rods resulted in lengths with a standard deviation of 4.7 cm. At the 0.10 significance level, test the claim that the new production method has lengths with a standard deviation different from 3.5 cm, which was the standard deviation for the old method. State the null and alternative hypotheses.

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7. (Refer to Question 6) Find the test statistic.

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8. (Refer to Question 6) Find the critical value(s) and state and explain the decision about the null hypothesis.

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9. (Refer to Question 6) State conclusion in non-technical terms.

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10. (Refer to Question 6) Calculate and show the confidence interval based on the significance level given above. Are the results the same as in question 8 and 9?

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