Question

Use the data to calculate the sample variance,
*s*^{2}. (Round your answer to five decimal
places.)

* n* = 10:

19.1, 9.5, 11.8, 8.8, 10.8, 8.8, 7.0, 12.6, 14.8, 12.4

*s*^{2} =

Construct a 95% confidence interval for the population variance,
*σ*^{2}. (Round your answers to two decimal
places.)

? to ?

Test *H*_{0}: *σ*^{2} = 9
versus *H*_{a}: *σ*^{2} >
9 using *α* = 0.05.

State the test statistic. (Round your answer to two decimal places.)

*χ*^{2} =

State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to four decimal places.)

χ^{2} |
> | |

χ^{2} |
< |

Answer #1

variance, s2 = 12.22711

α = 1 - 0.95 = 0.05

The critical values for α = 0.05 and df = 9 are Χ^2(1-α/2,n-1) =
2.7 and Χ^2(α/2,n-1) = 19.023

CI = (9*3.4967^2/19.023 , 9*3.4967^2/2.7)

CI = (5.78 , 40.76)

Test statistic,

Χ^2 = (n-1)*s^2/σ^2

Χ^2 = (10 - 1)*12.22711/9

Χ^2 = 12.23

Rejection Region

This is right tailed test, for α = 0.05 and df = 9

Critical value of Χ^2 is 16.919

Hence reject H0 if Χ^2 > 16.919

χ2 > 16.919

χ2 < NONE

Consider the following. n = 22, x = 126.4, s2 = 21.7, Ha: σ2
> 15, α = 0.05 Test H0: σ2 = σ02 versus the given alternate
hypothesis.
State the test statistic. (Round your answer to two decimal
places.)
χ2 =
State the rejection region. (If the test is one-tailed, enter
NONE for the unused region. Round your answers to two decimal
places.)
χ2 >
χ2 <
Construct a (1 − α)100% confidence interval for σ2
using the χ2...

Consider the following.
n = 22, x = 126.2,
s2 = 21.5,
Ha: σ2 > 15,
α = 0.05
Test H0: σ2 =
σ02 versus the given alternate
hypothesis.
State the test statistic. (Round your answer to two decimal
places.)
χ2 =
State the rejection region. (If the test is one-tailed, enter
NONE for the unused region. Round your answers to two decimal
places.)
χ2
>
χ2
<
Construct a (1 − α)100% confidence interval for σ2
using the χ2...

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(a) Find the mean and standard deviation of these data. (Round
your standard deviation to four decimal places.)
mean
standard deviation
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mean μ. (Round your answer to three decimal places.)
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Ha: μ < 7.5. Use α =
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xx
3.6
5.6
9.3
5.5
9.1
1.2
yy
8.9
19.3
22
12.6
27.7
10.5

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the claim, the grower sprays 200 trees with the new spray and 200
other trees with the standard spray. The following data were
recorded.
New Spray
Standard Spray
Mean Yield per Tree
(lb)
240
228
Variance s2
980
807
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container, but also the variation in potency values must be small.
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of 5 ± 0.1 milligram per cubic centimeter (mg/cc). A random sample
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−1, 7, 7, 5, 12
variance
22
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?

Find the standard deviation for the given sample data. Round
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49, 67, 35, 46, 76, 55, 40, 42, 38
answers:
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C. 6.2
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