Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information.
x  0.336  0.296  0.340  0.248  0.367  0.269 
y  3.2  7.5  4.0  8.6  3.1  11.1 
(b) Use a 10% level of significance to test the claim that ρ ≠ 0. (Use 2 decimal places.)
t  
critical t ± 
(d) Find the predicted percentage of strikeouts for a player with an x = 0.288 batting average. (Use 2 decimal places.)
%
(e) Find a 95% confidence interval for y when x = 0.288. (Use 2 decimal places.)
lower limit  % 
upper limit  % 
(f) Use a 10% level of significance to test the claim that β ≠ 0. (Use 2 decimal places.)
t  
critical t ± 
(g) Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.)
lower limit  
upper limit 
please show steps and work
x  76  64  63  80  63  67 
y  51  42  50  47  42  44 
Verify that ∑x = 413, ∑y = 276, ∑x^{2} = 28,699, ∑y^{2} = 12,774, ∑xy = 19,068, and r = 0.482, and find the Pvalue for the test that claims ρ is greater zero.
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
x  67  64  75  86  73  73 
y  42  39  48  51  44  51 
(a) Find Σx, Σy, Σx^{2}, Σy^{2}, Σxy, and r. (Round r to three decimal places.)
(b) Use a 5% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)
t =  
critical t = 
Conclusion
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 =  
critical t = 
Conclusion
15  17  16  20  14  11  15  18  16  12 
Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.72. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient’s doctor are as follows.
4.9  4.2  4.5  4.1  4.4  4.3 
(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)
x  =  
s  = 
(ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.72? Use ? = 0.05.
Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean ? = 8050 and estimated standard deviation ? = 2650. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.
(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
x 
67 
70 
69 
81 
65 
86 
y 
51 
54 
45 
56 
50 
49 
Given that ∑x = 438, ∑y = 305, ∑x^{2} = 32,332, ∑y^{2} = 15,579, ∑xy = 22,302, and r = 0.226, find the Pvalue for a test claiming that ρ is greater than zero.
0.25 > Pvalue > 0.10 

0.10 > Pvalue > 0.05 

0.40 > Pvalue > 0.25 

Pvalue < 0.0005 

Pvalue > 0.40X 
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
x 
87 
88 
70 
84 
78 
76 
y 
53 
57 
50 
51 
46 
50 
Given that S_{e} ≈ 3.054, a ≈ 16.547, b ≈ 0.425, and , find the predicted percentage of successful field goals for a player with x = 73% successful free throws.
31.0% 

5.1% 

28.0% 

47.6% 

14.5% 
The Student’s t distribution table gives critical values for the Student’s t distribution. Use an appropriate d.f. as the row header. For a righttailed test, the column header is the value of ? found in the onetail area row. For a lefttailed test, the column header is the value of ? found in the onetail area row, but you must change the sign of the critical value t to −t. For a twotailed test, the column header is the value of ? from the twotail area row. The critical values are the ±t values shown.
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4†. A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that x = 7.9 with sample standard deviation s = 1.5. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to three decimal places.)
test statistic  =  
critical value  = ± 
x 
63 
79 
70 
80 
84 
87 
y 
46 
49 
45 
55 
57 
58 
Find S_{e}. Round your answer to three decimal places.
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
x  67  64  75  86  73  73 
y  42  39  48  51  44  51 
Find the predicted percentage of successful field goals for a player with x = 65% successful free throws. (Round your answer to two decimal places.)
(e) Find a 90% confidence interval for y when x = 65. (Round your answers to one decimal place.)
lower limit  % 
upper limit  % 
(f) Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.)
t  
critical t 
(g) Find a 90% confidence interval for β. (Round your answers to three decimal places.)
lower limit  
upper limit 
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.8 with sample standard deviation s = 3.3. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
(a) Find Σx, Σy, Σx^{2}, Σy^{2}, Σxy, and r. (Round r to three decimal places.)
(b) Use a 5% level of significance to test the claim that ρ > 0. (Round your answers to two decimal places.)
Conclusion Reject the null hypothesis, there is sufficient evidence that ρ > 0.Reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0.Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0.
(c) Find S_{e}, a, b, and x. (Round your answers to four decimal places.)
(d) Find the predicted percentage ŷ of successful field goals for a player with x = 65% successful free throws. (Round your answer to two decimal places.) (e) Find a 90% confidence interval for y when x = 65. (Round your answers to one decimal place.)
(f) Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.)
Conclusion Reject the null hypothesis, there is sufficient evidence that β > 0.Reject the null hypothesis, there is insufficient evidence that β > 0. Fail to reject the null hypothesis, there is insufficient evidence that β > 0.Fail to reject the null hypothesis, there is sufficient evidence that β > 0.



Let X be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then X has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the X distribution is about 4.84. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient’s doctor are as follows.
4.6  4.7  4.7  4.5  4.5  4.1 
(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)
x  =  
s  = 
(ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.84? Use ? = 0.05.
and the alternate hypothesis
.
: μ —Select— ≥ ≤ > ≠ < =
: μ —Select— ≠ < = ≥ > ≤
(b) What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Compute the Pvalue. (Round your answer to four decimal places.)
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
(e) Interpret your conclusion in the context of the application.
14  19  17  20  15  12  13  18  17  10 
and the alternate hypothesis
.
: μ —Select— < = ≤ > ≠ ≥
: μ —Select— > = ≥ ≤ < ≠
and the alternate hypothesis
.
: μ —Select— ≤ < > ≠ ≥ =
: μ —Select— ≥ < > ≤ = ≠
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.4 with sample standard deviation s = 2.7. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
x  67  64  75  86  73  73 
y  44  41  48  51  44  51 
Σx  =__ 
Σy  =__ 
Σx^{2}  =__ 
Σy^{2}  =__ 
Σxy  =__ 
r  =__ 
(b) Use a 5% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)
t  =__ 
critical t=__ 
(c) Verify that S_{e} ≈ 2.7729, a ≈ 14.783, b ≈ 0.4345, and x ≈ 73.000.
S_{e}  =__ 
a  =__ 
b  =__ 
x  =__ 
(d) Find the predicted percentage of successful field goals for a player with x = 71% successful free throws. (Round your answer to two decimal places.)
__ %
(e) Find a 90% confidence interval for y when x = 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=__  
critical t=__ 
(g) Find a 90% confidence interval for ?. (Round your answers to three decimal places.)
lower limit  =__ 
upper limit=__ 
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 55.0 kg and standard deviation ? = 8.4 kg. Suppose a doe that weighs less than 46 kg is considered undernourished.
(b) If the park has about 2850 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does
(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 52 kg. If the average weight is less than 52 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight
(d) Compute the probability that
Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6250 and estimated standard deviation σ = 2950. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.
(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)
(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with sample standard deviation s = 2.7. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.
a. What is the value of the sample test statistic? (Round your answer to three decimal places.)
Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information.
x  0.338  0.306  0.340  0.248  0.367  0.269 
y  3.5  7.7  4.0  8.6  3.1 
11.1 
Σx = 1.868, Σy = 38, Σx^{2} = 0.592034, Σy^{2} = 294.32, Σxy = 11.1556, and r ≈ 0.901.
Use a 10% level of significance to test the claim that ρ ≠ 0. (Use 2 decimal places.)
t  
critical t ± 
Conclusion
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
x  67  64  75  86  73  73 
y  42  39  48  51  44  51 
lower limit  
upper limit 
Interpret its meaning.
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. Σx = 438, Σy = 275, Σx^{2} = 32264, Σy^{2} = 12727, Σxy = 20231, and r ≈ 0.827.
x  67  64  75  86  73  73 
y  42  39  48  51  44  51 
Use a 5% level of significance to test the claim that ρ > 0. (Round your answers to two decimal places.)
t  
critical t 
Conclusion
lower limit  % 
upper limit  % 
Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.)
t  
critical t 
Conclusion
lower limit  
upper limit 
Interpret its meaning.
Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6650 and estimated standard deviation σ = 2150. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.
(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?
What is the probability of x < 3500? (Round your answer to four decimal places.)
(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?
If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?
Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in July in a town in Colorado. The x distribution has a mean ? of approximately 75°F and standard deviation ? of approximately 8°F. A 20year study (620 July days) gave the entries in the rightmost column of the following table.
I  II  III  IV 
Region under Normal Curve 
x°F  Expected % from Normal Curve 
Observed Number of Days in 20 Years 
μ – 3σ ≤ x < μ – 2σ  51 ≤ x < 59  2.35%  15 
μ – 2σ ≤ x < μ – σ  59 ≤ x < 67  13.5%  90 
μ – σ ≤ x < μ  67 ≤ x < 75  34%  205 
μ ≤ x < μ + σ  75 ≤ x < 83  34%  213 
μ + σ ≤ x < μ + 2σ  83 ≤ x < 91  13.5%  86 
μ + 2σ ≤ x < μ + 3σ  91 ≤ x < 99  2.35%  11 
Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 8200 and estimated standard deviation σ = 3000. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.
(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)
What is the probability of x < 3500? (Round your answer to four decimal places.)
(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean ? = 69 and estimated standard deviation ? = 28. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.
(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)
(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.
What is the probability that x < 40? (Round your answer to four decimal places.)
(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 54.0 kg and standard deviation ? = 7.8 kg. Suppose a doe that weighs less than 45 kg is considered undernourished.
(b) If the park has about 2100 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
__ does
(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 51 kg. If the average weight is less than 51 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 40 does is less than 51 kg (assuming a healthy population)? (Round your answer to four decimal places.)
(d) Compute the probability that x < 55.2 kg for 40 does (assume a healthy population). (Round your answer to four decimal places.)
Suppose park rangers captured, weighed, and released 40 does in December, and the average weight was x = 55.2 kg. Do you think the doe population is undernourished or not? Explain.
x  73  74  80  66  77  77 
y  50  52  45  46  52  53 
Verify that S_{e} ≈ 3.694, a ≈ 38.254, b ≈ 0.153, and , ∑x =447, ∑y =298, ∑x^{2} =33,419, and ∑y^{2} =14,858, and use a 5% level of significance to find the Pvalue for the test that claims that β is greater than zero.
Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in January for a town in Hawaii. The x variable has a mean μ of approximately 68°F and standard deviation σ of approximately 4°F. A 20year study (620 January days) gave the entries in the rightmost column of the following table.
I  II  III  IIII 
Region under Normal Curve  x°F  Expected % from Normal Curve  Observed Number of Days in 20 Years 
μ – 3σ ≤ x < μ – 2σ  56 ≤ x < 60  2.35%  19 
μ – 2σ ≤ x < μ – σ  60 ≤ x < 64  13.5%  78 
μ – σ ≤ x < μ  64 ≤ x < 68  34%  202 
μ ≤ x < μ + σ  68 ≤ x < 72  34%  220 
μ + σ ≤ x < μ + 2σ  72 ≤ x < 76  13.5%  87 
μ + 2σ ≤ x < μ + 3σ  76 ≤ x < 80  2.35%  14 
(ii) Use a 1% level of significance to test the claim that the average daily January temperature follows a normal distribution with μ = 68 and σ = 4.
(c) Find or estimate the Pvalue of the sample test statistic. (Round your answer to three decimal places.)
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
x  67  64  75  86  73  73 
y  42  39  48  51  44  51 
(e) Find a 90% confidence interval for y when x = 65. (Round your answers to one decimal place.)
lower limit  % 
upper limit  % 
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
x  67  64  75  86  73  73 
y  42  39  48  51  44  51 
(c) Find S_{e}, a, b, and x. (Round your answers to four decimal places.)
(d) Find the predicted percentage ŷ of successful field goals for a player with x = 65% successful free throws. (Round your answer to two decimal places.)
(f) Use a 5% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)
t =  
critical t = 
Conclusion
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
x  69  66  63  65  76  76 
y  54  53  51  43  47  45 
Verify that S_{e} ≈ 4.739, a ≈ 67.050, b ≈ –0.263, and , ∑x =415, ∑y =293, ∑x^{2} =28,863, and ∑y^{2} =14,409, and find a 90% confidence interval for β and interpret its meaning. Round your final answers to three decimal places.
x  89  64  82  82  72  64 
y  61  47  56  47  53  48 
Verify that S_{e} ≈ 4.443, a ≈ 22.133, b ≈ 0.396, and , ∑x = 453, ∑y = 312, ∑x^{2} = 34,745, and ∑y^{2} = 16,388, and find a 98% confidence interval for y when x = 81. Round your final answers to one decimal place.
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