QUESTION #1
The method of tree-ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.
1,299 | 1,229 | 1,215 | 1,257 | 1,268 | 1,316 | 1,275 | 1,317 | 1,275 |
(a)
Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s.
(b)
Find a 90% confidence interval for the mean of all tree-ring dates from this archaeological site.
QUESTION # 2
How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (pounds):
68 | 106 | 129 | 125 | 60 | 64 |
Assume that the population of x values has an approximately normal distribution.
(a) Use a calculator with mean and sample standard deviation keys to find the sample mean weight x and sample standard deviation s. (Round your answers to one decimal place.)
x = | _____ lb |
s = | ______ lb |
(b) Find a 75% confidence interval for the population average
weight μ of all adult mountain lions in the specified
region. (Round your answers to one decimal place.)
lower limit | _________ lb |
upper limit | _________ lb |
Question 1
Values ( X ) | Σ ( Xi- X̅ )2 | |
1299 | 711.1129 | |
1229 | 1877.7749 | |
1215 | 3287.1073 | |
1257 | 235.1101 | |
1268 | 18.7775 | |
1316 | 1906.7807 | |
1275 | 7.1113 | |
1317 | 1995.1141 | |
1275 | 7.1113 | |
Total | 11451 | 10046.0001 |
Part a)
Mean X̅ = Σ Xi / n
X̅ = 11451 / 9 = 1272.3333
Sample Standard deviation SX = √ ( (Xi - X̅
)2 / n - 1 )
SX = √ ( 10046.0001 / 9 -1 ) = 35.4366
Part b)
Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.1 /2, 9- 1 ) = 1.86
1272.3333 ± t(0.1/2, 9 -1) * 35.4366/√(9)
Lower Limit = 1272.3333 - t(0.1/2, 9 -1) 35.4366/√(9)
Lower Limit = 1250.3626
Upper Limit = 1272.3333 + t(0.1/2, 9 -1) 35.4366/√(9)
Upper Limit = 1294.304
90% Confidence interval is ( 1250.3626 , 1294.304
)
Question 2
Values ( X ) | Σ ( Xi- X̅ )2 | |
68 | 576 | |
106 | 196 | |
129 | 1369 | |
125 | 1089 | |
60 | 1024 | |
64 | 784 | |
Total | 552 | 5038 |
Part a)
Mean X̅ = Σ Xi / n
X̅ = 552 / 6 = 92
Sample Standard deviation SX = √ ( (Xi - X̅
)2 / n - 1 )
SX = √ ( 5038 / 6 -1 ) = 31.7
Part b)
Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.25 /2, 6- 1 ) = 1.301
92 ± t(0.25/2, 6 -1) * 31.7/√(6)
Lower Limit = 92 - t(0.25/2, 6 -1) 31.7/√(6)
Lower Limit = 75.2
Upper Limit = 92 + t(0.25/2, 6 -1) 31.7/√(6)
Upper Limit = 108.8
75% Confidence interval is ( 75.2 , 108.8 )
QUESTION #1 The method of tree-ring dating gave the following years A.D. for an archaeological excavation...
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The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution. 1229 1194 1229 1201 1268 1316 1275 1317 1275 (a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.) x = A.D. s = yr (b) Find a 90% confidence interval for...
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The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution. 1313 1222 1187 1243 1268 1316 1275 1317 1275 (a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.) x = s = (b) Find a 90% confidence interval for the mean...
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