Reference no: EM131757043

Questions -

Q1. Match each of the descriptions on the left with the lettered word or phrase that it best defines. Each latter may be used once, or not at all.

- The value that is added to, and subtracted from a point estimate in order to create an interval estimate of some population parameter.	A. β
	B. Type I error
	C. Alternative hypothesis
- Rejecting the null hypothesis, when in fact it is true.	D. Range/4
	E. α
- A mathematical statement about the values of some population parameter that always allows equality.	F. Type II error
	G. Margin of Error
	H. Confidence Interval
- The probability that you make a type I error in a hypothesis test.	I. Confidence Coefficient
	J. Null hypothesis

Q2. In Ohio, drivers are required to carry motor vehicle insurance. Suppose that historical evidence shows that 12% of Ohio drivers do NOT carry motor vehicle insurance. If a simple random sample of 75 Ohio drivers contained 10 drivers who did NOT have motor vehicle insurance, then calculate the value of the test statistic that this data would produce for this hypothesis test on p.

TS:

Q3. The time that married men with children spend on child care averages about 6.4 hours per week. Suppose that you belong to a professional group on family practices that would like to do its own study to determine if the time that married men in your area differs from the reported mean of 6.4 hours per week. If the data collected produced a value of Z_O that yielded a PV = 0.059, then write out your Decision and Conclusion at the 1% level. Remember to justify your decision.

D/C:

Q4. Because of high production-changeover time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of $220 per hour. A research study will measure the cost of the new method over a sample production period.

Write out the most appropriate null and alternative hypotheses for this study.

H_O:

H_A:

Q5. Researchers believe that the average weekly earnings for men in managerial and professional positions is $725 and they are interested in testing the claim that women in the same positions have average weekly earnings that are significantly less than those for men.

Set up the correct pair of hypotheses that should be used to test this claim.

H_O:

H_A:

Q6. Suppose that you collected data to test the following alternative hypothesis:

H_A: μ<100

and that the data produced Z_O = -1.93. Calculate the PV for this test statistic.

P_V:

Q7. Over the past decade it is believed that the average total commuting distance to and from work has significantly increased. If the average total commuting distance to and from work was 35 miles a decade ago, then specify the form of the Rejection Region for your hypothesis test. Assume that you do NOT know the population standard deviation for the total commuting times, that you have 33 drivers in your sample, and that you will be using a 5% level of significance.

RR:

Q8. A 2005 work force study found that 12.5% of U.S. workers belonged to a union. Since that time unions have been engaged in activities designed to get more U.S. workers to join their ranks. If a simple random sample of 400 U.S. workers conducted in 2008 had 52 who belonged to a union, then complete the following full hypothesis test to determine if union membership has increased significantly since 2005:

H_O:

H_A:

α:

TS:

RR:

D⁄C:

PV:

Q9. If a 99% CI for μ₁ - μ₂ was determined to be: (-11.575, 2.983), what conclusion do you draw about how μ₁ and μ₂ compare to each other? BE SPECIFIC and EXPLAIN how this CI leads to your conclusion.

10. A production line operates with a mean filling weight of 16 ounces per container. Overfilling or under-filling presents a serious problem and when detected requires the operator to shut down the production line to readjust the filling mechanism. To test for overfilling or under-filling the following hypothesis test is performed at regular intervals throughout the day:

H_O: μ = 16

H_A: μ ≠ 16

a. Describe exactly what a Type I Error would be using the language of this problem.

b. If a Type II Error occurred when the hypothesis test was performed, would the operator shut down the production line for readjustment? EXPLAIN.

Q11. Calculate the p-value for the following pair of hypotheses:

a. H_O: μ₁ - μ₂ ≤ 0

H_A: μ₁ - μ₂ > 0

TS: T₀ = 2.211, with 58 df.

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