The following data were obtained with a cascade impactor: D, (um) G (%) 0.5 5.4 1.0 14.4 23.4 37.0 55.1 2.0 4.0 8.0
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- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?A group of six, obese adult men had their weights recorded both before and 10 months after having a diet treatment to help manage their weight. Observe the information presented in the table below: The weights of six obese adult men both before and 10-months after having a diet treatment Before Diet Treatment After Diet Treatment 250 240 225 215 220 198 311 300 326 298 205 205 Test at α = 0.05 the hypothesis that for the group, there was a statistically significant average decrease in weight from before diet treatment to 10 months after. Hint: This is hypothesis testing for paired samples. Here, you will use a paired t test.
- The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. Weekly Gross Revenue ($1000s) Televison Advertising ($1000s) Newspaper Advertising ($1000s) 97 6 1.5 90 2 2 95 5 1.5 93 3.5 2.5 95 3 4.3 95 3.5 3.3 95 3.5 4.2 95 4 2.5 a. Use alpha= 0.01 to test the hypotheses Ho : Beta Sub1= Beta Sub2 =0 Ha : Beta Sub1 and/or Beta Sub2 is not equal to zero for the model y=Beta Sub 0+ Beta Sub1 Xsub1+Beta Sub2 Xsub2+E , where X1= television advertising ($1000s) X2+ newspaper advertising ($1000s) Compute the F test statistic (to 2 decimals). Use F table. What is the p-value? - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2 What is your conclusion? - Select your answer -The overall model is not significantThe overall model is significantItem 3 b. Use alpha =0.05 to…Draw a scatter diagram for the data and determine by inspection if there exists an approximate linear relationship between Y and X. Approximately draw a straight-line between the plotted values. State the general relationship between Y and disposable X in1.exact linear form 2. stochastic form.Demand for haircut at PogiPoints Barber Shop has increased steadily for the past few months as seen in the following time series data. Do the necessary computations and choose the best answer that would complete each statement. With MAD as the criterion, the best forecasting model for this time series data is: * A.)Naïve approach B.)2-week SMA C).WMA with weights: 0.5, 0.3, 0.2 D). D. ES with alpha = 0.8
- The type of battery in Jim's laptop has a lifetime X (in years) which follows a Weibull distribution with parameters α=2 and β=4. The type of battery in Jim's tablet has a lifetime Y (in years) which follows an exponential distribution with parameter λ=1/4.Find E(XY−2Y).(Answer as a decimal number, and round to 2 decimal places).As a bonus assignment a former student checked if your professor gave a statisticallysignificant difference in grades between his male and female students. She based herstudy based on grades assigned in intermediate Econ courses (Econ 303, 305 and 317)and her sample included nm = 485 male students and nf = 264 female students. Theaverage grades received were xm = 84.6 and xf = 85.8 The population standad deviation were σ m = 12.0 and σ f = 11.4 8. From the same extra-credit study as in question 7 see above, this former student found that the proportion of female students in principle courses (Econ 203, 205) was ?̅? = 0.380, while the proportion of female students in intermediate courses (Econ 303, 305, 317) was ?̅? = 0.352. The principle courses sample size was np = 782, while the intermediate courses sample size was ni = 749. Test the hypothesis that female students are less in intermediate courses using a 90% confidence level and the p-value approach.The body mass index (BMI) of a person is defined to be the person’s body mass divided by the square of the person’s height. The article “Influences of Parameter Uncertainties within the ICRP 66 Respiratory Tract Model: Particle Deposition” (W. Bolch, E. Farfan, et al., Health Physics, 2001:378–394) states that body mass index (in kg/m²) in men aged 25–34 is lognormally distributed with parameters μ = 3.215 and σ = 0.157. a) Find the mean BMI for men aged 25–34. b) Find the standard deviation of BMI for men aged 25–34. c) Find the median BMI for men aged 25–34. d) What proportion of men aged 25–34 have a BMI less than 22? e) Find the 75th percentile of BMI for men aged 25–34.
- Suppose your dependent variable is aggregate household demand for electricity for various cities. To correct for heteroskedasticity you should Select one: a. multiply observations by the square root of the city size b. multiply observations by the city size c. divide observations by the city size d. divide observations by the square root of the city size e. none of theseBelow is the SPSS output for the relationship between height at age 3 (X) and at age 20 (Y). Correlations heightAt3 heightAt20 heightAt3 Pearson Correlation 1 .840** Sig. (2-tailed) .000 N 16 16 heightAt20 Pearson Correlation .840** 1 Sig. (2-tailed) .000 N 16 16 **. Correlation is significant at the 0.01 level (2-tailed). ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 236.838 1 236.838 33.628 .000b Residual 98.599 14 7.043 Total 335.438 15 Dependent Variable: heightAt20 Predictors: (Constant), heightAt3 Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 41.679 4.470 9.325 .000 heightAt3 .664 .114 .840 5.799 .000 Dependent Variable: heightAt20 State hypothesis for the…Suppose your dependent variable is crime rates for various cities. To correct for heteroskedasticity you should Select one: a. multiply observations by the city size b. multiply observations by the square root of the city size c. none of these d. divide observations by the square root of the city size e. divide observations by the city size
