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- 8.6 Husbands and wives, Part I. The Great Britain Office of Population Census and Surveys once collest data on a random sample of 170 married couples in Britain, recording the age (in years) and beich (converted here to inches) of the husbands and wives.° The scatterplot on the left shows the wife's plotted against her husband's age, and the plot on the right shows wife's height plotted against husbandie height. 70 65 40 20- 55- 40 60 60 65 70 75 20 Husband's age (in years) Husband's height (in inches) (a) Describe the relationship between husbands' and wives' ages. (b) Describe the relationship between husbands' and wives' heights. (c) Which plot shows a stronger correlation? Explain your reasoning. (d) Data on heights were originally collected in centimeters, and then converted to inches. Does this con- version affect the correlation between husbands' and wives' heights? Wife's age (in years) Wife's height (in inches)Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. 203 x days y km/100 72 76 32 14.7 94 11.7 19.5 5.3 35.6 (a) Verify that Ex = 477, Ey = 86.8, Ex? = 62,029, Ey2 = 2028.68, Exy = 11036.6, and r= 0.93853. Ex Ey Ex? Ey2| Exy (b) Use a 1% level of significance to test the claim p> 0. (Use 2 decimal places.) critical t Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. Reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is insufficient evidence that p > 0. O…1) What is the line of best fit for this data? a. y =-1.11x+ 11.83; r=-0.9760964904 Average Speed (mi/h) Time (hours) b. y 11.83x- 1. 11; r=0.9527643586 8.5 2.5 c. y= 11.83x –- 1. 11; r=-0.9760964904 7.5 3.75 d. y =-1.11x+ 11.83; r= 0.9527643586. 6.5 4.5 6.0 5.0 5.5 5.5 5.0 6.25 4.0 6.75 3.5 8.75 r notes MacBook Pro * 2$ & 4 5 6 7 8 9. %3D deletc { [ Y ] G H J K L > ? C V N M + || .. .. B
- Radon is a gas emitted from the ground that can collect in houses in buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered “acceptable” Radon levels in a house vary from week to week. In one house, a sample of 6 weeks had the following readings for radon level (in pCi/L): 1.9 2.8 3.9 3.9 4.2 5.7 Find the variance and standard deviation (definitional formula). Show your work using a table."Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. "Wrinkle recovery angle" measures how well a fabric recovers from wrinkles. Higher is better. Here are data on the wrinkle recovery angle (in degrees) for two types of treated fabrics: Permafresh 12 13 15 11 10 16 14 Hylite 14 19 20 16 A manufacturer wants to know how large is the difference in mean wrinkle recovery angle. Give a 98% confidence interval for the difference in mean wrinkle recovery angle: [three decimal accuracy] [three decimal accuracy]Systolic coefficients of variation are 14.2% and the Diastolic is 17% The coefficients of variation for each data set are: a. more than 5 percentage points apart b. within 5 percentage points of each other Therefore, the systolic measurements vary a. about the same as b. significantly more than c. significantly less than the diastolic measurements.
- A researcher is interested in testing the relationship between smoking and BMI (kg/m2) in adults aged 30-45. In order to test this association, the researcher divides smoking into currently more than a pack a day, currently less than a pack a day, and never smokers. The following table represents the BMIs for each participant enrolled by their respective smoking category. Current Smoker (≥1pack/day) Current Smoker (<1 pack/day Never Smoked 26.7 29.4 22.1 29.4 28.6 30.4 24.3 27.4 21.3 28.4 23.2 26.4 21.6 20.1 19.7 27.4 20.6 19.8 26.8 19.7 21.6 36.4 19.6 22.3 31.5 21.6 24.3 27.4 21.5 *Continue as though all assumptions for ANOVA are met. A) Calculate the MSW and MSB for the data represented above. B) Carry out a formal test for a one-way analysis of variance among the groups and interpret your results.Water is poured into a large, cone-shaped cistern. The volume of water, measured in cm, is reported at Which of the following would linearize the data for volume and time? different time intervals, measured in seconds. The scatterplot of volume versus time showed a curved Seconds, cm3 O In(Seconds), cm3 Seconds, In(cm') pattern. O In(Seconds), In(cm³)The correlation between height and weight of a sample of 100 individuals is calculated to be 0.8 using Pearson's r. What can we conclude about the relationship between height and weight in the population from which the sample was taken?
- "Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. "Wrinkle recovery angle" measures how well a fabric recovers from wrinkles. Higher is better. Here are data on the wrinkle recovery angle (in degrees) for two types of treated fabrics: Permafresh Hylite 15 17 12 14 13 16 16 15 14 18 A manufacturer wants to know how large is the difference in mean wrinkle recovery angle. Give a 98% confidence interval for the difference in mean wrinkle recovery angle: [three decimal accuracy] [three decimal accuracy]Q1. A study was conducted to investigate the relationship between premature birth and mental development at 12 months. The infant's birth weight was used as an index of prematurity. At age 12 months, the child's mental development was recorded. The results are shown below (the weights are in pounds): Birth 4 6 7 8 Weight(x) Developmental 85 Quotients(y) 88 87 94 96 Summary: n = 5, £x=30, £x² = 190, Ey= 450, Ey² = 40590, Exy = 2728 . a. Find the least square prediction equation, y on x. b. Obtain a 95% confidence interval for the average value of y when x 6.5 (i.e., a C.I. for E(y|x= 6.5)). c. Obtain the coefficient of correlation (r) and interpret the result. d. Test the hypothesis that H, :p= 0 vs. H, : p0. Use a =0.05.Suppose that a customer is purchasing a car. He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 Sample mean for Car 2 x= 245 mi / 10 gal (Type an integer or decimal rounded to one decimal place as needed.) times on each car and records the number of miles driven. Full data set Car 1 Median for Car 1 M= mi / 10 gal (Type an integer or decimal rounded to one decimal place as needed.) 245 242 215 244 220 265 291 160 284 251 169 319 257 306 267 Car 2 Median for Car 2 230 242 M=O mi / 10 gal 206 214 236 256 245 255 241 264 (Type an integer or decimal rounded to one decimal place as needed.) 276 252 250 251 257