# Very urgent math homework

math stats dq hw

questio1

14.81 Corvette Prices. Following are the age and price data for Corvettes from Exercise 14.17. age 6 6 6 2 2 5 4 5 1 4

price 290 280 295 425 384 315 355 328 425 325

a. Obtain a point estimate for the mean price of all 4-year-old Corvettes.

b. Determine a 90% confidence interval for the mean price of all 4-year-old Corvettes.

c. Find the predicted price of a 4-year-old Corvette.

d. Determine a 90% prediction interval for the price of a 4-year- old Corvette.

Question2

14.85 Study Time and Score. Following are the data on to- tal hours studied over 2 weeks and test score at the end of the 2 weeks from Exercise 14.21.

x 10 15 12 20 8 16 14 22

y 92 81 84 74 85 80 84 80

a. Determine a point estimate for the mean test score of all be- ginning calculus students who study for 15 hours.

b. Find a 99% confidence interval for the mean test score of all beginning calculus students who study for 15 hours.

c. Find the predicted test score of a beginning calculus student who studies for 15 hours.

d. Determine a 99% prediction interval for the test score of a beginning calculus student who studies for 15 hours.

Question3

Samples

a-1,3,5

b-0,6,2,5,2

c-3,12,6,3

a. Obtain the sample mean and sample standard deviation of each of the three samples.

b. Obtain SST, SSTR, andSSE by using the defining formulas and verify that the one-way ANOVA identity holds.

c. Obtain SST, SSTR,andSSE by using the computing formulas.

d. Construct the one-way ANOVA table.

Qn4

8.7 Fuel Tank Capacity. Consumer Reports provides informa- tion on new automobile models—including price, mileage rat- ings, engine size, body size, and indicators of features. A simple random sample of 35 new models yielded the following data on fuel tank capacity, in gallons.

17.2 23.1 17.5 15.7 19.8 16.9 15.3 18.5 18.5 25.5 18.0 17.5 14.5 20.0 17.0 20.0 24.0 26.0 18.1 21.0 19.3 20.0 20.0 12.5 13.2 15.9 14.5 22.2 21.1 14.4 25.0 26.4 16.9 16.4 23.0

a. Find a point estimate for the mean fuel tank capacity of all new automobile models. Interpret your answer in words. (Note: x i = 664.9 gallons.)

b. Determine a 95.44% confidence interval for the mean fuel tank capacity of all new automobile models. Assume σ = 3.50 gallons.

c. How would you decide whether fuel tank capacities for new automobile models are approximately normally distributed?

d. Must fuel tank capacities for new automobile models be ex- actly normally distributed for the confidence interval that you obtained in part (b) to be approximately correct? Explain your answer. 8.8 Home Improvements. The American Express Retail Index

qn 5

pooled t-statistic-

Let’s use σ to denote the common standard deviation of the two populations. We know from Key Fact 10.1 on page 394 that, for independent samples, the standardized version of ¯x 1 −¯x 2 , z = ( ¯x 1 −¯x 2 ) − (μ 1 − μ 2 ) √ , (σ1 2/n 1) + (σ2 2/n 2)

10.56 Simulation. In this exercise, you are to perform a computer simulation to illustrate the distribution of the pooled t-statistic, given above

a. Simulate 1000 random samples of size 4 from a normally dis- tributed variable with a mean of 100 and a standard deviation of 16. Then obtain the sample mean and sample standard de- viation of each of the 1000 samples.

b. Simulate 1000 random samples of size 3 from a normally dis- tributed variable with a mean of 110 and a standard deviation of 16. Then obtain the sample mean and sample standard de- viation of each of the 1000 samples.

c. Determine the value of the pooled t-statistic for each of the 1000 pairs of samples obtained in parts (a) and (b).

d. Obtain a histogram of the 1000 values found in part (c). e. Theoretically, what is the distribution of all possible values of the pooled t-statistic? f. Compare your results from parts (d) and (e).

qn 6

Working with Large Data Sets In each of Exercises 12.59–12.61,

use the technology of your choice to solve the specified problems.

12.59 Governors. The National Governors Association pub- lishes information on U.S. governors in Governors’ Political Affiliations & Terms of Office. Based on that document, we obtained the data on region of residence and political party given on the WeissStats CD.

a. Group the bivariate data for these two variables into a contin- gency table.

b. Determine the conditional distribution of region within each party and the marginal distribution of region.

c. Determine the conditional distribution of party within each re- gion and the marginal distribution of party.

d. Are the variables “region” and “party” for U.S. governors as- sociated? Explain your answer.

Qn 7

12.60 Motorcycle Accidents.

The Scottish Executive, Analyti- cal Services Division Transport Statistics, compiles information on motorcycle accidents in Scotland. During one year, data on the number of motorcycle accidents, by day of the week and type of road (built-up or non built-up), are as presented on the WeissStats CD.

a. Group the bivariate data for these two variables into a contin- gency table.

b. Determine the conditional distribution of day of the week within each type-of-road category and the marginal distribu- tion of day of the week.

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