# DAT 565 Practice Week 4 Exercise

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1. Concerned about graffiti, mayors of nine suburban communities instituted a citizen Community Watch program.

(a) Choose the appropriate hypotheses to see whether the number of graffiti incidents declined. Assume μd is the mean difference in graffiti incidents before and after.

(b) Find the test statistic tcalc. (A negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

(c) State the critical value tcrit for α = .05. (A negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

(d) Find the p-value. (Round your answer to 4 decimal places.)

(e) State your conclusion.

1. Do a two-sample test for equality of means assuming unequal variances. Calculate the p-value using Excel.

(a-1) Comparison of GPA for randomly chosen college juniors and seniors:

(a-2) Based on the above data choose the correct decision.

(b-1) Comparison of average commute miles for randomly chosen students at two community colleges:

(b-2) Based on the above data choose the correct decision.

(c-1) Comparison of credits at time of graduation for randomly chosen accounting and economics students:

(c-2) Based on the above data choose the correct decision.

1. A certain company will purchase the house of any employee who is transferred out of state and will handle all details of reselling the house. The purchase price is based on two assessments, one assessor being chosen by the employee and one by the company. Based on the sample of eight assessments shown, do the two assessors agree? Use the .01 level of significance.

(a) Choose the appropriate hypotheses. Assume d = company assessed value – employee assessed value.

(b) State the decision rule for .01 level of significance.

(c-1) Find the test statistic tcalc. (

(c-2) What is your conclusion?

1. A certain company will purchase the house of any employee who is transferred out of state and will handle all details of reselling the house. The purchase price is based on two assessments, one assessor being chosen by the employee and one by the company. Based on the sample of eight assessments shown, do the two assessors agree? Use the .05 level of significance.

(a) Choose the appropriate hypotheses. Assume d = company assessed value – employee assessed value.

(b) State the decision rule for .05 level of significance. (Round your answers to 2 decimal places. A negative value should be indicated by a minus sign.)

(c-1) Find the test statistic tcalc. (Round your answer to 2 decimal places. A negative value should be indicated by a minus sign.)

(c-2) What is your conclusion?

1. The XYZ Corporation is interested in possible differences in days worked by salaried employees in three departments in the financial area. A survey of 23 randomly chosen employees reveals the data shown below. Because of the casual sampling methodology in this survey, the sample sizes are unequal. Research question: Are the mean annual attendance rates the same for employees in these three departments?

1. High blood pressure, if untreated, can lead to increased risk of stroke and heart attack. A common definition of hypertension is diastolic blood pressure of 90 or more.

(a) State the null and alternative hypotheses for a physician who checks your blood pressure.

(b) Type I error occurs when the physician concludes a patient has high blood pressure when the patient does not. The consequence is unnecessary treatment and worry. Type II error occurs when the physician concludes that a patient's blood pressure is okay when it is too high. The consequence is untreated high blood pressure, which can lead to serious health complications.

1. The number of entrees purchased in a single order at a Noodles & Company restaurant has had a historical average of 1.35 entrees per order. On a particular Saturday afternoon, a random sample of 26 Noodles orders had a mean number of entrees equal to 1.4 with a standard deviation equal to 0.7. At the 1 percent level of significance, does this sample show that the average number of entrees per order was greater than expected?

(a) Choose the correct null and alternative hypotheses.

(b-1) Calculate the t statistic. (Round your answer to 2 decimal places.)

(b-2) Find the p-value. (Round your answer to 4 decimal places.)

(c) Choose the correct conclusion.

1. GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.54 mg of mercury. A sample of 40 bulbs shows a mean of 3.62 mg of mercury.

(a) State the hypotheses for a right-tailed test, using GreenBeam’s claim as the null hypothesis about the mean.

(b) Assuming a known standard deviation of 0.17 mg, calculate the z test statistic to test the manufacturer’s claim. (Round your answer to 2 decimal places.)

(c) At the 10 percent level of significance (α = .10) does the sample exceed the manufacturer’s claim?

(d) Find the p-value. (Round intermediate calculations to 2 decimal places. Round your answer to 4 decimal places.)

1. This table shows partial results for a one-factor ANOVA.

(a) Calculate the F test statistic. (Round your answer to 4 decimal places.)

(b) Calculate the p-value using Excel’s function =F.DIST.RT(F, DF1, DF2). (Round your answer to 4 decimal places.)

(c) Find the critical value F.05 from Appendix F or using Excel’s function =F.INV.RT(.05, DF1, DF2). (Round your answer to 2 decimal places.)

(d) Interpret the results.

1. The lifespan of xenon metal halide arc-discharge bulbs for aircraft landing lights is normally distributed with a mean of 1,900 hours and a standard deviation of 580 hours.

(a) If a new ballast system shows a mean life of 2,316 hours in a test on a sample of 13 prototype new bulbs, would you conclude that the new lamp’s mean life exceeds the current mean life at α = 0.10?

(b) What is the p-value? (Round your answer to 4 decimal places.)

1. One group of accounting students used simulation programs, while another group received a

a. Construct a 90 percent confidence interval for the true difference in mean scores. (Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.)

b. Do you think the learning methods have significantly different results?

1. The mean arrival rate of flights at O'Hare Airport in marginal weather is 195 flights per hour with a historical standard deviation of 14 flights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days of marginal weather, the mean arrival rate is 202 flights per hour.

(a) Set up a right-tailed decision rule at α = .025 to decide whether there has been a significant increase in the mean number of arrivals per hour. Choose the appropriate hypothesis.

(b-1) Calculate the test statistic. (Round your answer to 2 decimal places.)

(b-2) What is the conclusion?

(b-3) Would the decision have been different if you used α = .01?

1. A small dealership leased 21 Suburu Outbacks on 2-year leases. When the cars were returned at the end of the lease, the mileage was recorded (see below).

(a) Is the dealer's mean significantly greater than the national average of 30,291 miles for 2-year leases? Using the 10 percent level of significance, choose the appropriate hypothesis.

(b) Calculate the test statistic. (Round your answer to 2 decimal places.)

(c) The dealer's cars show a significantly greater mean number of miles than the national average at the 10 percent level.

1. A quality standard says that no more than 2 percent of the eggs sold in a store may be cracked (not broken, just cracked). In 3 cartons (12 eggs each carton), 2 eggs are cracked.

(a) Calculate a p-value for the observed sample result. Hint: Use Excel to calculate the cumulative binomial probability P(X ≥ 2 | n = 36, ππ = .02) = 1 – P(X ≤ 1 | n = 36, ππ = .02). (Round your answer to 4 decimal places.)

(b) We fail to reject the null hypothesis at α = .10.

(c) This sample shows that the standard is exceeded.

1. A ski company in Vail owns two ski shops, one on the west side and one on the east side of Vail. Ski hat sales data (in dollars) for a random sample of 5 Saturdays during the 2004 season showed the following results. Is there a significant difference in sales dollars of hats between the west side and east side stores at the 10 percent level of significance?

(a) Choose the appropriate hypotheses. Assume μd is the difference in average sales between the east side and west side stores.

(b) State the decision rule for a 5 percent level of significance. (Round your answers to 3 decimal places.)

(c-1) Find the test statistic tcalc. (Round your answer to 2 decimal places. A negative value should be indicated by a minus sign.)

(c-2) What is your conclusion?

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