1. Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. An archaeological study provides data relatingx= body diameter in centimeters andy= height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data.

Predictor	Coef	SE Coef	T	P
Constant	-0.182	2.429	-0.09	0.929
Diameter	0.8013	0.1471	4.15	0.003
S =4.07980 R-Sq = 74.2%

(a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height? diameterheight (b) For the least-squares line=a+bx, what is the value of the constanta? What is the value of the slopeb? (Note: The slope is the coefficient of the predictor variable.) Write the equation of the least-squares line.

a=

b=

= + x

(c) TheP-value for a two-tailed test corresponding to each coefficient is listed underP. Thetvalue corresponding to the coefficient is listed underT. What is theP-value of the slope? What are the hypotheses for a two-tailed test of= 0? H₀:< 0;H₁:= 0H₀:= 0;H₁:0 H₀:= 0;H₁:< 0H₀:0;H₁:= 0H₀:= 0;H₁:> 0 Based on theP-value in the printout, do we reject or fail to reject the null hypothesis for= 0.01? Reject the null hypothesis. There is sufficient evidence thatdiffers from 0.Fail to reject the null hypothesis. There is insufficient evidence thatdiffers from 0. Fail to reject the null hypothesis. There is sufficient evidence thatdiffers from 0.Reject the null hypothesis. There is insufficient evidence thatdiffers from 0. (d) Recall that thetvalue and resultingP-value of the slopebequal thetvalue and resultingP-value of the corresponding correlation coefficientr. To find the value of the sample correlation coefficientr, take the square root of the "R-Sq" value shown in the display. What is the value ofr? (Round your answer to three decimal places.) Consider a two-tailed test forr. Based on theP-value shown in the Minitab display, is the correlation coefficient significant at the 1% level of significance? No, the correlation coefficient is not significant at the= 0.01 level because theP-value.Yes, the correlation coefficient is significant at the= 0.01 level because theP-value >. Yes, the correlation coefficient is significant at the= 0.01 level because theP-value.No, the correlation coefficient is not significant at the= 0.01 level because theP-value >.

2.

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.

x	67	64	75	86	73	73
y	42	39	48	51	44	51

(a) Verify thatx=438,y=275,x²=32264,y²=12727,xy=20231, andr0.827.

x
y
x2
y2
xy
r

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

t
criticalt

ConclusionReject the null hypothesis, there is sufficient evidence that> 0.Reject the null hypothesis, there is insufficient evidence that> 0. Fail to reject the null hypothesis, there is insufficient evidence that> 0.Fail to reject the null hypothesis, there is sufficient evidence that> 0.

(c) Verify thatS_e3.1191,a6.564,b0.5379, andx73.000.

Se
a
b
x

(d) Find the predicted percentageof successful field goals for a player withx=83%successful free throws. (Round your answer to two decimal places.) % (e) Find a 90% confidence interval forywhenx=83. (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
criticalt

ConclusionReject the null hypothesis, there is sufficient evidence that> 0.Reject the null hypothesis, there is insufficient evidence that> 0. Fail to reject the null hypothesis, there is insufficient evidence that> 0.Fail to reject the null hypothesis, there is sufficient evidence that> 0.

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

lower limit
upper limit

Interpret its meaning. For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls within the confidence interval.For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls within the confidence interval. For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls outside the confidence interval.For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls outside the confidence interval.

3.

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.

x	0.310	0.298	0.340	0.248	0.367	0.269
y	2.9	7.9	4.0	8.6	3.1	11.1

(a) Verify thatx=1.832,y=37.6,x²=0.569058,y²=293.6,xy=10.8696, andr-0.815.

x
y
x2
y2
xy
r

(b) Use a5%level of significance to test the claim that0. (Use 2 decimal places.)

t
criticalt

ConclusionReject the null hypothesis, there is sufficient evidence thatdiffers from 0.Reject the null hypothesis, there is insufficient evidence thatdiffers from 0. Fail to reject the null hypothesis, there is insufficient evidence thatdiffers from 0.Fail to reject the null hypothesis, there is sufficient evidence thatdiffers from 0.

(c) Verify thatS_e2.2048,a25.523, andb-63.065.

Se
a
b

(d) Find the predicted percentageof strikeouts for a player with anx=0.32batting average. (Use 2 decimal places.) % (e) Find a90%confidence interval forywhenx=0.32. (Use 2 decimal places.)

lower limit	%
upper limit	%

(f) Use a5%level of significance to test the claim that0. (Use 2 decimal places.)

t
criticalt

ConclusionReject the null hypothesis, there is sufficient evidence thatdiffers from 0.Reject the null hypothesis, there is insufficient evidence thatdiffers from 0. Fail to reject the null hypothesis, there is insufficient evidence thatdiffers from 0.Fail to reject the null hypothesis, there is sufficient evidence thatdiffers from 0.

(g) Find a90%confidence interval forand interpret its meaning. (Use 2 decimal places.)

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upper limit

Interpretation For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls within the confidence interval.For every unit increase in batting average, the percentage strikeouts increases by an amount that falls within the confidence interval. For every unit increase in batting average, the percentage strikeouts increases by an amount that falls outside the confidence interval.For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls outside the confidence interval.

4.

What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Letx= depth of divein meters, and lety= optimal timein hours. A random sample of divers gave the following data.

x	12.1	26.3	29.2	38.3	51.3	20.5	22.7
y	2.68	2.38	1.78	1.03	0.75	2.38	2.20

(a) Findx,y,x²,y²,xy, andr. (Roundrto three decimal places.)

x	=
y	=
x2	=
y2	=
xy	=
r	=

(b) Use a 1% level of significance to test the claim that< 0. (Round your answers to two decimal places.)

t	=
criticalt	=

Conclusion Reject the null hypothesis. There is insufficient evidence that< 0.Fail to reject the null hypothesis. There is insufficient evidence that< 0. Fail to reject the null hypothesis. There is sufficient evidence that< 0.Reject the null hypothesis. There is sufficient evidence that< 0.

(c) FindS_e,a, andb. (Round your answers to five decimal places.)

Se	=
a	=
b	=

(d) Find the predicted optimal time in hours for a dive depth ofx=30meters. (Round your answer to two decimal places.) hr (e) Find an 80% confidence interval forywhenx=30meters. (Round your answers to two decimal places.)

lower limit	hr
upper limit	hr

(f) Use a 1% level of significance to test the claim that< 0. (Round your answers to two decimal places.)

t	=
criticalt	=

Conclusion Reject the null hypothesis. There is sufficient evidence that< 0.Reject the null hypothesis. There is insufficient evidence that< 0. Fail to reject the null hypothesis. There is insufficient evidence that< 0.Fail to reject the null hypothesis. There is sufficient evidence that< 0.

(g) Find a 90% confidence interval forand interpret its meaning. (Round your answers to three decimal places.)

lower limit
upper limit

Interpretation For a 1 meter increase in depth, the optimal time decreases by an amount that falls within the confidence interval.For a 1 meter increase in depth, the optimal time decreases by an amount that falls outside the confidence interval. For a 1 meter increase in depth, the optimal time increases by an amount that falls outside the confidence interval.For a 1 meter increase in depth, the optimal time increases by an amount that falls within the confidence interval.

5.

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).

x	6.7	4.9	4.2	3.3	2.1	(units: mm Hg/10)
y	44.0	32.9	26.2	16.2	13.9	(units: mm Hg/10)

(a) Verify thatx=21.2,y=133.2,x²=101.84,y²=4160.5,xy=648.7, andr0.981.

x
y
x2
y2
xy
r

(b) Use a10%level of significance to test the claim that> 0. (Use 2 decimal places.)

t
criticalt

ConclusionReject the null hypothesis, there is sufficient evidence that> 0.Reject the null hypothesis, there is insufficient evidence that> 0. Fail to reject the null hypothesis, there is insufficient evidence that> 0.Fail to reject the null hypothesis, there is sufficient evidence that> 0.

(c) Verify thatS_e2.7475,a-3.135, andb7.022.

Se
a
b

(d) Find the predicted pressure when breathing pure oxygen if the pressure from breathing available air isx=5.1. (Use 2 decimal places.) (e) Find a99%confidence interval forywhenx=5.1. (Use 1 decimal place.)

lower limit
upper limit

(f) Use a10%level of significance to test the claim that> 0. (Use 2 decimal places.)

t
criticalt

ConclusionReject the null hypothesis, there is sufficient evidence that> 0.Reject the null hypothesis, there is insufficient evidence that> 0. Fail to reject the null hypothesis, there is insufficient evidence that> 0.Fail to reject the null hypothesis, there is sufficient evidence that> 0.

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

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upper limit

Interpretation For a one-unit increase in oxygen pressure breathing only available air, the oxygen pressure breathing pure oxygen increases by an amount that falls within the confidence interval.For a one-unit increase in oxygen pressure breathing only available air, the oxygen pressure breathing pure oxygen decreases by an amount that falls within the confidence interval. For a one-unit increase in oxygen pressure breathing only available air, the oxygen pressure breathing pure oxygen increases by an amount that falls outside the confidence interval.For a one-unit increase in oxygen pressure breathing only available air, the oxygen pressure breathing pure oxygen decreases by an amount that falls outside the confidence interval.

6.

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.

xdays	71	79	31	94	208
ykm/100	14.9	19.5	5.3	11.9	35.6

(a) Verify that

x=483,

y=87.2,

x²=64,343,

y²=2039.32,

xy=11286.1,

and

r0.94527.

x
y
x2
y2
xy
r

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

> 0.

(Use 2 decimal places.)

t
criticalt

ConclusionReject the null hypothesis, there is sufficient evidence that> 0.Reject the null hypothesis, there is insufficient evidence that> 0. Fail to reject the null hypothesis, there is insufficient evidence that> 0.Fail to reject the null hypothesis, there is sufficient evidence that> 0.

(c) Verify that

S_e4.2898,

a1.8040,

and

b0.1619.

Se
a
b

(d) Find the predicted distance (km/100) when a drift bottle has been floating for80days. (Use 2 decimal places.) km/100 (e) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.)

lower limit	km/100
upper limit	km/100

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

> 0.

(Use 2 decimal places.)

t
criticalt

ConclusionReject the null hypothesis, there is sufficient evidence that> 0.Reject the null hypothesis, there is insufficient evidence that> 0. Fail to reject the null hypothesis, there is insufficient evidence that> 0.Fail to reject the null hypothesis, there is sufficient evidence that> 0.

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

lower limit
upper limit

Interpretation For every day of drift, the distance drifted decreases by an amount that falls within the confidence interval.For every day of drift, the distance drifted increases by an amount that falls within the confidence interval. For every day of drift, the distance drifted increases by an amount that falls outside the confidence interval.For every day of drift, the distance drifted decreases by an amount that falls outside the confidence interval.

(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. After40days,how far from the accident site should a rescue plane expect to look? (Use 2 decimal places.) km/100