1.Letxbe a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Letybe a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample ofn= 6 professional basketball players gave the following information.

x676475867373

y444148514451

(a) Verify thatx=438,y=279,x²=32264,y²=13059,xy=20493, andr0.800.

(b) Use a 5% level of significance to test the claim that> 0. (Round your answers to two decimal places.)]

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criticalt

e) Find a 90% confidence interval forywhenx=71. (Round your answers to one decimal place.)

lower limit%

upper limit%

(f) Use a 5% level of significance to test the claim that> 0. (Round your answers to two decimal places.)

t

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g) Find a 90% confidence interval for. (Round your answers to three decimal places.)

lower limit

upper limit

2.Letxbe a random variable that represents the batting average of a professional baseball player. Letybe a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample ofn= 6 professional baseball players gave the following information.

x0.3260.2780.3400.2480.3670.269

y3.57.24.08.63.111.1

(a) Verify thatx=1.828,y=37.5,x²=0.567714,y²=286.87,xy=10.759, andr-0.885.

(b) Use a10%level of significance to test the claim that0. (Use 2 decimal places.)

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(d) Find the predicted percentage of strikeouts for a player with anx=0.324batting average. (Use 2 decimal places.)

%

(e) Find a95%confidence interval forywhenx=0.324. (Use 2 decimal places.)

lower limit%

upper limit%

(f) Use a10%level of significance to test the claim that0. (Use 2 decimal places.)

t

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g) Find a95%confidence interval forand interpret its meaning. (Use 2 decimal places.)

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upper limit

3.

Aviation and high-altitude physiology is a specialty in the study of medicine. Letx= partial pressure of oxygen in the alveoli (air cells in the lungs) when breathing naturally available air. Lety= partial pressure when breathing pure oxygen. The (x, y) data pairs correspond to elevations from 10,000 feet to 30,000 feet in 5000 foot intervals for a random sample of volunteers. Although the medical data were collected using airplanes, they apply equally well to Mt. Everest climbers (summit 29,028 feet).

x7.15.54.23.32.1(units: mm Hg/10)

y42.434.326.216.213.9(units: mm Hg/10)

(a) Verify thatx=22.2,y=133,x²=113.6,y²=4116.34,xy=682.38, andr0.985.

(b) Use a1%level of significance to test the claim that> 0. (Use 2 decimal places.)

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(d) Find the predicted pressure when breathing pure oxygen if the pressure from breathing available air isx=5.3. (Use 2 decimal places.)

(e) Find a99%confidence interval forywhenx=5.3. (Use 1 decimal place.)

lower limit

upper limit

(f) Use a1%level of significance to test the claim that> 0. (Use 2 decimal places.)

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(g) Find a99%confidence interval forand interpret its meaning. (Use 2 decimal places.)

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4.

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. Letxrepresent the number of days to recovery of a drift bottle after release andyrepresent 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

.xdays72743297205

ykm/10014.919.65.711.935.1

(a) Verify thatx=480,

y=87.2,

x²=63,118,

y²=2012.28,

xy=11055.4,

andr0.92755.

(b) Use a 1% level of significance to test the claim> 0.

(Use 2 decimal places.)

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(d) Find the predicted distance (km/100) when a drift bottle has been floating for70days. (Use 2 decimal places.)

km/100

(e) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.)

lower limitkm/100

upper limitkm/100

(f) Use a 1% level of significance to test the claim that> 0.

(Use 2 decimal places.)

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criticalt

(g) Find a 95% confidence interval forand interpret its meaning in terms of drift rate. (Use 2 decimal places.)

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(h) Consider the following scenario. A sailboat had an accident and radioed a Mayday alert with a given latitude and longitude just before it sank. The survivors are in a small (but well-provisioned) life raft drifting in the part of the Pacific Ocean under study. After30days,how far from the accident site should a rescue plane expect to look? (Use 2 decimal places.)

km/100