Question
In: Statistics and Probability
Suppose, for a random sample selected from a normal population, we have the values of the...
Suppose, for a random sample selected from a normal population,
we
have the values of the sample mean x ̄ = 67.95 and the standard
deviation s = 9.
a. Construct a 95% confidence interval for population mean μ
assuming the sample size n = 16.
b. Construct a 90% confidence interval for population mean μ
assuming n = 16.
c. Obtain the width of the confidence intervals calculated in a and
b. Is the width of 90% confidence
interval (calculated in part a) smaller than the width of 95%
confidence interval (calculated in
part b). If so, why? Explain.
d. Find the 95% confidence interval for μ assuming n = 25.
e. Is the width of 95% confidence interval (calculated in part d)
smaller than the width of 95%
confidence interval (calculated in part a). If so, why?
Explain.
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A random sample from a normal population yields the following 25 values:
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A random sample of size n1 = 16 is selected from a normal population with a...
A random sample of size n1 = 16 is selected
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taken from another normal population with mean 68 and standard
deviation 11. Let X1and X2 be the two sample means. Find:
(a) The probability that X1-X2 exceeds 4.
(b) The probability that 4.8 ≤X1-X2≤ 5.6.
Round your answers to two decimal places (e.g. 98.76).
A random sample of size n1 = 14 is selected from a normal population with a...
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deviation 14. Let X¯1and X¯2 be the two sample means. Find:
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Suppose that a random sample of size 64 is to be selected from a population with...
Suppose that a random sample of size 64 is to be selected from a
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Suppose that a random sample of size 64 is to be selected from a population with...
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A random sample of n =100 is selected from a normal population with mean μ =...
A random sample of n =100 is selected from a normal
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Find the probability that is less than 24.3
Suppose you have selected a random sample of ?=13 measurements from a normal distribution. Compare the...
Suppose you have selected a random sample of ?=13 measurements
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?=
?=
(b) 90% confidence interval
?=
?=
(c) 99% confidence interval
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Suppose we take a random sample X1,…,X5 from a normal population with unknown variance σ2 and...
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Suppose we take a random sample X1,…,X5 from a normal population with an unknown variance σ2...
Suppose we take a random sample X1,…,X5 from a normal population
with an unknown variance σ2 and unknown mean μ.
Construct a two-sided 95% confidence interval for σ2 if the
observations are given by
−1.25,1.91,−0.09,2.71,2.70
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