Question
In: Statistics and Probability
A random sample of n = 100 measurements is selected from a population with unknown mean...
A random sample of n = 100 measurements is selected from a
population with unknown mean µ and known standard deviation σ = 10.
(a) (1 point) Calculate the width of a 90% confidence interval for
µ.
(b) Calculate the width of a 95% confidence interval for µ.
(c) (Calculate the width of a 99% confidence interval for µ.
(d) Based on the above results, what effect does increasing the
confidence coefficient have on the width of the confidence
interval.
Solutions
orchestra answered 2 years agoRelated Solutions
A random sample of n measurements was selected from a population with unknown mean μ and...
A random sample of n measurements was selected from a population
with unknown mean μ and standard deviation σ=35 for each of the
situations in parts a through d. Calculate a 95% confidence
interval for muμ
for each of these situations.
a. n=75, x overbarx=22
b. n=150,x overbarxequals=110
c. n=90, x overbarxequals=18
d. n=90,x overbarxequals=4.69
e. Is the assumption that the underlying population of
measurements is normally distributed necessary to ensure the
validity of the confidence intervals in parts a...
A random sample of n measurements was selected from a population with unknown mean μ and...
A random sample of n measurements was selected from a population
with unknown mean μ and standard deviation σ = 15 for each of the
situations in parts a through d. Calculate a 99% confidence
interval for μ for each of these situations.
a. n = 75, x̄ = 27
b. n = 150, x̄ = 105
c. n = 125, x̄ = 16
d. n = 125, x̄ = 5.37
e. Is the assumption that the underlying population of...
A random sample of n measurements was selected from a population with unknown mean m and...
A random sample of n measurements was selected from a population
with unknown mean m and standard deviation
σ=20σ=20
. Calculate a 99% confidence interval for
μμ
for each of the following situations:
a. n=75,x¯¯¯=28 b. n=200,x¯¯¯=102 c. n=100,x¯¯¯=15 d.
n=100,x¯¯¯=4.05 a. n=75,x¯=28 b.
n=200,x¯=102 c. n=100,x¯=15 d.
n=100,x¯=4.05
e. Is the assumption that the underlying population of
measurements is normally distributed necessary to ensure the
validity of the confidence intervals in parts a–d ? Explain.
A random sample of n measurements was selected from a population with unknown mean mu and...
A random sample of n measurements was selected from a population
with unknown mean mu and standard deviation sigma equals 20 for
each of the situations in parts a through d. Calculate a 95%
confidence interval for mu for each of these situations.
a. n=60, overbar =29 (Round to two decimal places as
needed.)
b. n=250, xoverbare=113 (Round to two decimal places as
needed.)
c. n=90, xoverbar=18 (Round to two decimal places as
needed.)
d. n=90, xoverbar=4.1 (Round to two...
A random sample of n measurements was selected from a population with standard deviation σ=13.6and unknown...
A random sample of n measurements was selected from a population
with standard deviation σ=13.6and unknown mean μ. Calculate a 90 %
confidence interval for μ for each of the following situations:
(a) n=35, x=78.5
(b) n=50, x¯=78.5
(c)n=70, x¯=78.5
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
population with mean μ = 24 and standard deviation
σ = 1.25.
Find the probability that is less than 24.3
A random sample of ?n measurements was selected from a population with standard deviation 13.913.9 and...
A random sample of ?n measurements was selected from a
population with standard deviation 13.913.9 and unknown mean ?μ.
Calculate a 9999 % confidence interval for ?μ for each of the
following situations:
(a) ?=35, ?⎯⎯⎯=104.9n=35, x¯=104.9
(b) ?=60, ?⎯⎯⎯=104.9n=60, x¯=104.9
(c) ?=85, ?⎯⎯⎯=104.9n=85, x¯=104.9
(d) In general, we can say that for the same confidence level,
increasing the sample size the margin of error (width)
of the confidence interval. (Enter: ''DECREASES'', ''DOES NOT
CHANGE'' or ''INCREASES'', without the quotes.)
A random sample of ?n measurements was selected from a population with standard deviation ?=14.6 and...
A random sample of ?n measurements was selected from a
population with standard deviation ?=14.6 and unknown mean ?.
Calculate a 99% confidence interval for ? for each of the following
situations:
(a) ?=45, ?⎯⎯⎯=76.3
____ ≤?≤ _______
(b) ?=65, ?⎯⎯⎯=76.3
____ ≤?≤ ______
(c) ?=85, ?⎯⎯⎯=76.3
______ ≤?≤ _______
A random sample of ?n measurements was selected from a population with standard deviation ?=11.7 and...
A random sample of ?n measurements was selected from a
population with standard deviation ?=11.7 and unknown mean ?.
Calculate a 95% confidence interval for ? for each of the following
situations:
(a) ?=60, ?=85
≤?≤
(b) ?=75, ?=85
≤?≤
(c) ?=100, ?=85
≤?≤
A random sample of n = 100 scores is selected from a normal population with a...
A random sample of n = 100 scores is selected from a normal
population with a mean of μ = 60 and a standard deviation of σ =
20. What is the probability of obtaining a sample mean greater than
M = 57?
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