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# null and alternative hypotheses

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1. An printout of the descriptive measures of daily checking account balances (in \$) of bank customers is shown below. Develop a 95% confidence interval estimate for the mean of the population of the checking balances.

Account Balance Information
Mean 4828.29
Median 5115.25
Mode 4976.50
Standard Deviation 1143.57
Sample Variance 1307763.49
Kurtosis 8.63
Skewness -3.06
Range 4968.50
Minimum 600.00
Maximum 5568.50
Sum 173818.50
Count 36.00

Solution must include background work including formulas if necessary.

2. A survey of a college (population 25,450) showed that 870 of 1100 students sampled supported a fee increase to fund improvements to the library. Using the 95% level of confidence, what is the confidence interval for the true proportion which support the fee increase?

Solution must include background work including formulas if necessary.

3. You are in charge of benefits at a company. You have a national medical insurance plan for your company's employees which provides for either 100% of the usual and customary rates for a variety of surgical procedures or the actual charge, whichever is lower. Records are retained of the actual charges by procedure, and for most surgical procedures the average actual charge is close to the usual and customary rate defined by the insurer. You have noticed a discrepancy, however, between the average actual charge and customary rate for childbirths by C-section. The usual customary rate is at \$1,200 and the average of the actual charges based on a sample of 32 cases is only \$1,150 with a sample standard deviation of \$300. You are concerned about discrepancies in both directions. Since your insurance fees are experience-rated, if the usual and customary rates were set too high, your company would be paying too much. If the insurer's usual and customary rates were set too low, your employees might view their compensation package as inadequate.

A. Test at the 5% significance level whether there is a problem with the customary rate.

B. What is the null and alternative hypotheses?

C. Work through the hypothesis test, what conclusion do you reach?

D. What is the p-value?

4. You manufacture fur coats and you have purchased a truckload of 10,000 fur pelts. Your contract with the breeder specified that at least 10% of the pelts would be silver. Your workers have sorted and cleaned 1,000 of the pelts and they have found 85 silver pelts.

A. You want to test at the 5% significance level whether you received by contract an adequate supply of silver pelts.

B. What is the null and alternative hypotheses?

C. Work through the hypothesis test..what conclusion do you reach?

D. What is the p-value?

5. Conduct an analysis of variance test on the daily yields of four fund managers expressed on annualized basis (%).

Manager 1 Manager 2 Manager 3 Manager 4
20% 18% 29% 26%
16 24 19 21
15 18 17 19
14 12 19 17
11 13 16 14
15 13 19 18
20 14 16 21
17 11
14 19
11 10
A. ANVOA

B. What is the Null and Alternative Hypotheses?

D. What is the conclusion at a 5% significance level and why?

6. A manager for a steam cleaning equipment co. believes there is a relationship between city population and the amount of sales. To verify this belief, the following data was collected:

City Population (millions) Sales (\$ millions)
1 2.0 \$3.0
2 1.0 1.0
3 1.5 2.0
4 0.5 0.8
5 1.5 3.0
6 1.0 1.5
7 3.0 5.0
8 2.0 4.0

A. What is the value of coefficient of determination? Show background work and formulas if necessary.

B. What is the regression equation?
Show work.