Question

A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years): 2.0 1.2 6.0 1.7 5.3 0.4 1.0 5.3 15.7 0.6 4.8 0.9 12.3 5.3 0.6 (a) Assume that the lifetime distribution is exponential and use an argument parallel to that of this example to obtain a 95% CI for expected (true average) lifetime. (Round your answers to two decimal places.) (b) What is a 95% CI for the standard deviation of the lifetime distribution? [Hint: What is the standard deviation of an exponential random variable?] (Round your answers to two decimal places.)

Answer #1

A random sample of n = 15 heat pumps of a certain type
yielded the following observations on lifetime (in years):
2.0
1.5
6.0
1.7
5.2
0.4
1.0
5.3
15.7
0.5
4.8
0.9
12.2
5.3
0.6
(a) Assume that the lifetime distribution is exponential and use
an argument parallel to that of this example to obtain a 95% CI for
expected (true average) lifetime. (Round your answers to two
decimal places.)
________ and _________ years
(b.) What is a 95%...

A random sample of n = 15 heat pumps of a certain type yielded
the following observations on lifetime (in years):
2.0 1.5 6.0 1.8 5.3 0.4 1.0 5.3
15.6 0.8 4.8 0.9 12.4 5.3 0.6
(a) Assume that the lifetime distribution is exponential and use
an argument parallel to that of this example to obtain a 95% CI for
expected (true average) lifetime. (Round your answers to two
decimal places.( ................. , ......................)
years
(c) What is a 95%...

A random sample of n = 15 heat pumps of a certain type
yielded the following observations on lifetime (in years):
2.0
1.2
6.0
1.8
5.1
0.4
1.0
5.3
15.7
0.8
4.8
0.9
12.4
5.3
0.6
(a) Assume that the lifetime distribution is exponential and use
an argument parallel to that of this example to obtain a 95% CI for
expected (true average) lifetime. (Round your answers to two
decimal places.)
(b) How should the interval of part (a) be...

Solve the following using the t-distribution table:
A random sample of 15 heat pumps of a certain type yielded the
following observations on lifetime (in years): 2.0, 1.3, 6.0, 1.9,
5.1, 0.4, 1.0, 5.3, 15.7, 0.7, 4.8, 0.9, 12.2, 5.3, 0.6
a)For obtaining a 95% CI for expected (true average) lifetime,
what will be the maximum possible difference between sample mean
and true mean.
b) Obtain a 95% CI for expected (true average) lifetime.

A random sample of size n=25 from N(μ, σ2=6.25)
yielded x=60. Construct the following confidence intervals for μ.
Round all your answers to 2 decimal places.
a. 95% confidence interval:
95% confidence interval = 60 ± ?
b. 90% confidence interval:
90% confidence interval = 60 ± ?
c. 80% confidence interval:
80% confidence interval = 60 ± ?

A random sample of size n = 50 is selected from a
binomial distribution with population proportion
p = 0.8.
Describe the approximate shape of the sampling distribution of
p̂.
Calculate the mean and standard deviation (or standard error) of
the sampling distribution of p̂. (Round your standard
deviation to four decimal places.)
mean =
standard deviation =
Find the probability that the sample proportion p̂ is
less than 0.9. (Round your answer to four decimal places.)

1. The following data represent petal lengths (in cm) for
independent random samples of two species of Iris.
Petal length (in cm) of Iris virginica:
x1; n1 = 35
5.1
5.9
6.1
6.1
5.1
5.5
5.3
5.5
6.9
5.0
4.9
6.0
4.8
6.1
5.6
5.1
5.6
4.8
5.4
5.1
5.1
5.9
5.2
5.7
5.4
4.5
6.4
5.3
5.5
6.7
5.7
4.9
4.8
5.9
5.1
Petal length (in cm) of Iris setosa:
x2; n2 = 38
1.5
1.9
1.4
1.5
1.5...

Suppose a random sample of n = 25 observations is
selected from a population that is normally distributed with mean
equal to 108 and standard deviation equal to 14.
(a) Give the mean and the standard deviation of the sampling
distribution of the sample mean
x.
mean
standard deviation
(b) Find the probability that
x
exceeds 113. (Round your answer to four decimal places.)
(c) Find the probability that the sample mean deviates from the
population mean ? = 108...

Suppose a random sample of n = 16 observations is selected from
a population that is normally distributed with mean equal to 102
and standard deviation equal to 10.
a) Give the mean and the standard deviation of the sampling
distribution of the sample mean x.
mean =
standard deviation =
b) Find the probability that x exceeds 106. (Round your
answer to four decimal places.)
c) Find the probability that the sample mean deviates from the
population mean μ...

Consider a normal population with an unknown population standard
deviation. A random sample results in x−x− = 49.64 and
s2 = 38.44.
a. Compute the 95% confidence interval for
μ if x−x− and s2 were obtained from a
sample of 22 observations. (Round intermediate calculations
to at least 4 decimal places. Round "t" value to 3 decimal
places and final answers to 2 decimal places.)
b. Compute the 95% confidence interval for
μ if x−x− and s2 were obtained from...

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