What does the shaded (blue) region show? Shade in the regions for the (i) significance level (ii) wrongly accepting the Null-what type of error is this.
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- The population, P, of the city of Hazelton has grown according to the mathematical model P = 65,000(1.075)*, where t is the number of years since 2005. a) At what percentage is the population growing? b) If this trend continues, during which year will the population reach approx. 100,000?Accountants at the Tucson firm, Larry Youdelman,CPAs, believed that several traveling executives were submittingunusually high travel vouchers when they returned from businesstrips. First, they took a sample of 200 vouchers submitted from the past year. Then they developed the following multiple-regres-sion equation relating expected travel cost to number of days on the road ( x1 ) and distance traveled ( x2 ) in miles:yn = +90.00 + +48.50x1 + +.40x2The coefficient of correlation computed was .68.a) If Donna Battista returns from a 300-mile trip that took herout of town for 5 days, what is the expected amount she shouldclaim as expenses?b) Battista submitted a reimbursement request for $685. Whatshould the accountant do?c) Should any other variables be included? Which ones? Why?While rejecting H0 on a hypothesis test means that _______, measures of effect size tell you ______. how big an effect the treatment has; that the treatment has some effect that the treatment has some effect; how big an effect the treatment has that the treatment caused an increase; that the treatment caused a decrease d. that the treatment caused a decrease; that the treatment caused an increase
- A hat manufacturer is planning to expand its workforce. It estimates thatthe number of hats produced by hiring x new workers is given byT(x) = – 0.25 x4 + 6 x3 0 ≤ x ≤ 18a) When is the rate of change of hat production increasing and when is itdecreasing?b) What is the point of diminishing returns (Hint: inflection point) and themaximum rate of change of hat production?A house is purchased for $140,000 in January 2004. A year later, the house next door is sold for $149,800. The two houses are of the same style and size and are in similar condition, so they should have equal value.Use the model v = 140e0.0676586485t, where t is the number of years after January 2004 and v is the value in thousands of dollars, to predict when the house would be worth $290,000.With the gasoline time series data from table 17.1, show the exponential smoothing forecasts using a = .1.a. applying the MSe measure of forecast accuracy, would you prefer a smoothing constant of a = .1 or a = .2 for the gasoline sales time series?b. are the results the same if you apply Mae as the measure of accuracy?c. What are the results if Mape is used?
- (a) Find the value at risk (VaR) for an investment of $400,000 at2%. (That is, find out how low the value of this investment could be if the worst 2% of outcomes are ruled out.) The investment is expected to grow during the year by 10% with SD 35%. Assume a normal model for the change in value. (b) How much smaller would the annual SD of the investment need to become in order to reduce the VaR to $100,000? Assume that the expected growth remains 10%. (a) The value at risk (VaR) for an investment of $400,000 at 2% is _____ (Round to the nearest thousand dollars as needed.) (b) The annual SD of the investment would need to become _______%. (Round to four decimal places as needed.)The number of welfare cases in a city of population p is expected to be W = 0.006p4/3. If the population is growing by 1200 people per year, find the rate at which the number of welfare cases will be increasing when the population is p = 1,000,000.As baby boomers enter their golden years, the number of people afflicted with Alzheimer's disease is expected to rise dramatically. In a study published in the Journal of Neurology, the number of people with Alzheimer's disease in the United States age 65 years and over is projected to be N(t) = 0.00525t2 + 0.075t + 4.7 (0 ≤ t ≤ 4) million in decade t, where t = 0 corresponds to 2010.† (a)What is the projected number of people with Alzheimer's disease in the United States age 65 years and over in 2040? (Round your answer to four decimal places.) million (b) How fast is the number of people with Alzheimer's disease in the United States age 65 years and over projected to grow in 2040? million per decade (c)How fast is the rate of growth of people with Alzheimer's disease in the United States age 65 years and over projected to change in the period covered by the study? million per decade per decade
- Can you tell how old a lion is by looking at its nose? A professor at the University of Wisconsin-Madison con-ducted a study of data taken from 32 lions and observed the relationship between age (in years) and proportionof blackness in the lion’s nose. The equation of the leastsquares regression line was yn = 0.8790 + 10.6471x where yn is the predicted age of the lion, measured inyears, and x is the proportion of the lion’s nose that isblack. A lion whose nose was 11% black was known to be1.9 years old. What is the residual for the age of this lion?a) -0.15 years b) 0.15 yearsc) 0.88 years d) 2.05 yearse) 10.65 years(Source: http://www.stat.wisc.edu/~st571-1/15-regression-4.pdf)You run a multiple regression, and the p-value turns out be very small, about 0.001. Which of the following can you definitely conclude? a. The R-square value is not guaranteed to be large; it could be a value like 0.34. b. The p-values for the regression coefficients of all X variables will indicate significance at the 1% level. c. The p-value for the regression coefficient of at least one X variable will indicate significance at the 1% level. d. All of these choices are true.In this regression, which test statistic would you use to test the nullhypothesis that the regression function is linear against the alternativethat it is cubic? If the value of that statistic is 37.7 with associatedp-value 0.0001, what would your conclusion be?
