Q1 Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit vegetables cereals nuts corpse) Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million) A high phosphorous content may or may not indicate an ancient burial site, food storage site, or even a garbage dump Independent random samples from two regions gave the following phosphorous measurements (in ppm) Assume the distribution of phosphorous is mound shaped and symmetric for these two regions Region I x 1 n 1 15 853 1,549 1,230 875 1,080 2,330 1,850 1,860 2,340 1,080 910 1,130 1,450 1,260 1,010 Region II x 2 n 2 14 538 808 790 1,230 1,770 960 1,650 860 890 640 1,180 1,160 1,050 1,020 (a) Use a calculator with mean and standard deviation keys to verify that x 1 , s 1 , x 2 , and s 2 (Round your answers to four decimal places ) x 1 ppm s 1 ppm x 2 ppm s 2 ppm (b) Let 1 be the population mean for x 1 and let 2 be the population mean for x 2 Find an 80 confidence interval for 1 2 (Round your answers to one decimal place ) lower limitppm upper limitppm Q2 For large U S companies, what percentage of their total income comes from foreign sales A random sample of technology companies (IBM, Hewlett Packard, Intel, and others) gave the following information Technology companies, foreign revenue x 1 n 1 16 62 8 55 7 47 0 59 6 55 3 41 0 65 1 51 1 53 4 50 8 48 5 44 6 49 4 61 2 39 3 41 8 Another independent random sample of basic consumer product companies (Goodyear, Sarah Lee, H J Heinz, Toys 'R' Us) gave the following information Basic consumer product companies, foreign revenue x 2 n 2 17 28 0 30 5 34 2 50 3 11 1 28 8 40 0 44 9 40 7 60 1 23 1 21 3 42 8 18 0 36 9 28 0 32 5 Assume that the distributions of percentage foreign revenue are mound shaped and symmetric for these two company types (a) Use a calculator with mean and standard deviation keys to calculate x 1 , s 1 , x 2 , and s 2 (Round your answers to four decimal places ) x 1 s 1 x 2 s 2 (b) Let 1 be the population mean for x 1 and let 2 be the population mean for x 2 Find a95 confidence interval for 1 2 (Round your answers to two decimal places ) lower limit upper limit Q3 independent random samples of professional football and basketball players gave the following information Assume that the weight distributions are mound shaped and symmetric Weights (in lb) of pro football players x 1 n 1 21 243 262 254 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 272 Weights (in lb) of pro basketball players x 2 n 2 19 204 200 220 210 193 215 223 216 228 207 225 208 195 191 207 196 182 193 201 (a) Use a calculator with mean and standard deviation keys to calculate x 1 , s 1 , x 2 , and s 2 (Round your answers to four decimal places ) x 1 s 1 x 2 s 2 (b) Let 1 be the population mean for x 1 and let 2 be the population mean for x 2 Find a 99 confidence interval for 1 2 (Round your answers to one decimal place ) lower limit upper limit Q4 A random sample of382married couples found that292had two or more personality preferences in common In another random sample of574married couples, it was found that only22had no preferences in common Let p 1 be the population proportion of all married couples who have two or more personality preferences in common Let p 2 be the population proportion of all married couples who have no personality preferences in common (a) Find a90 confidence interval for p 1 p 2 (Use 3 decimal places lower limit upper limit Q5 Most married couples have two or three personality preferences in common A random sample of370married couples found that124had three preferences in common Another random sample of580couples showed that226had two personality preferences in common Let p 1 be the population proportion of all married couples who have three personality preferences in common Let p 2 be the population proportion of all married couples who have two personality preferences in common (a) Find a95 confidence interval for p 1 p 2 (Use 3 decimal places ) lower limit upper limit Q6 The U S Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987 Let x 1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952 Based on9180observations, the sample mean interval was x 1 65 0minutes Let x 2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987 Based on24,170observations, the sample mean time interval was x 2 70 8minutes Historical data suggest that 1 8 77minutes and 2 11 50minutes Let 1 be the population mean of x 1 and let 2 be the population mean of x 2 (a) Compute a95 confidence interval for 1 2 (Use 2 decimal places ) lower limit upper limit Q7 On the Navajo Reservation, a random sample of228permanent dwellings in the Fort Defiance region showed that64were traditional Navajo hogans In the Indian Wells region, a random sample of137permanent dwellings showed that21were traditional hogans Let p 1 be the population proportion of all traditional hogans in the Fort Defiance region, and let p 2 be the population proportion of all traditional hogans in the Indian Wells region (a) Find a90 confidence interval for p 1 p 2 (Use 3 decimal places ) lower limit upper limit

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Q1 Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables <

Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts < corpse). Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million). A high phosphorous content may or may not indicate an ancient burial site, food storage site, or even a garbage dump. Independent random samples from two regions gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two regions.

Region I:x₁;n₁= 15

853 1,549 1,230 875 1,080 2,330 1,850 1,860

2,340 1,080 910 1,130 1,450 1,260 1,010

Region II:x₂;n₂= 14

538 808 790 1,230 1,770 960 1,650 860

890 640 1,180 1,160 1,050 1,020

(a)

Use a calculator with mean and standard deviation keys to verify thatx₁,s₁,x₂, ands₂. (Round your answers to four decimal places.)

x₁=ppm

s₁=ppm

x₂=ppm

s₂=ppm

(b)

Let₁be the population mean forx₁and let₂be the population mean forx₂. Find an 80% confidence interval for₁₂.(Round your answers to one decimal place.)

lower limitppm

upper limitppm

For large U.S. companies, what percentage of their total income comes from foreign sales? A random sample of technology companies (IBM, Hewlett-Packard, Intel, and others) gave the following information.

Technology companies, % foreign revenue:x₁;n₁= 16

62.8 55.7 47.0 59.6 55.3 41.0 65.1 51.1

53.4 50.8 48.5 44.6 49.4 61.2 39.3 41.8

Another independent random sample of basic consumer product companies (Goodyear, Sarah Lee, H.J. Heinz, Toys 'R' Us) gave the following information.

Basic consumer product companies,% foreign revenue:x₂;n₂= 17

28.0 30.5 34.2 50.3 11.1 28.8 40.0 44.9

40.7 60.1 23.1 21.3 42.8 18.0 36.9 28.0

32.5

Assume that the distributions of percentage foreign revenue are mound-shaped and symmetric for these two company types.

(a) Use a calculator with mean and standard deviation keys to calculatex₁,s₁,x₂, ands₂. (Round your answers to four decimal places.)

x₁=%

s₁=%

x₂=%

s₂=%

(b) Let₁be the population mean forx₁and let₂be the population mean forx₂. Find a95%confidence interval for₁₂.(Round your answers to two decimal places.)

lower limit%

upper limit%

independent random samples of professional football and basketball players gave the following information. Assume that the weight distributions are mound-shaped and symmetric.Weights (in lb) of pro football players:x₁;n₁= 21

243 262 254 251 244 276 240 265 257 252 282

256 250 264 270 275 245 275 253 265 272

Weights (in lb) of pro basketball players:x₂;n₂= 19

204 200 220 210 193 215 223 216 228 207

225 208 195 191 207 196 182 193 201

(a) Use a calculator with mean and standard deviation keys to calculatex₁,s₁,x₂, ands₂. (Round your answers to four decimal places.)

x₁=

s₁=

x₂=

s₂=

(b) Let₁be the population mean forx₁and let₂be the population mean forx₂. Find a 99% confidence interval for₁₂.(Round your answers to one decimal place.)

lower limit

upper limit

A random sample of382married couples found that292had two or more personality preferences in common. In another random sample of574married couples, it was found that only22had no preferences in common. Letp₁be the population proportion of all married couples who have two or more personality preferences in common. Letp₂be the population proportion of all married couples who have no personality preferences in common.

(a) Find a90%confidence interval forp₁-p₂. (Use 3 decimal places.

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Most married couples have two or three personality preferences in common. A random sample of370married couples found that124had three preferences in common. Another random sample of580couples showed that226had two personality preferences in common. Letp₁be the population proportion of all married couples who have three personality preferences in common. Letp₂be the population proportion of all married couples who have two personality preferences in common.

(a) Find a95%confidence interval forp₁-p₂. (Use 3 decimal places.)

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The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Letx₁be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on9180observations, the sample mean interval wasx₁=65.0minutes. Letx₂be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on24,170observations, the sample mean time interval wasx₂=70.8minutes. Historical data suggest that₁=8.77minutes and₂=11.50minutes. Let₁be the population mean ofx₁and let₂be the population mean ofx₂.

(a) Compute a95%confidence interval for₁-₂. (Use 2 decimal places.)

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upper limit

On the Navajo Reservation, a random sample of228permanent dwellings in the Fort Defiance region showed that64were traditional Navajo hogans. In the Indian Wells region, a random sample of137permanent dwellings showed that21were traditional hogans. Letp₁be the population proportion of all traditional hogans in the Fort Defiance region, and letp₂be the population proportion of all traditional hogans in the Indian Wells region.

(a) Find a90%confidence interval forp₁-p₂. (Use 3 decimal places.)

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upper limit