Question
In: Statistics and Probability
Suppose we were to gather a random sample of 27 observations from a population and wished...
Suppose we were to gather a random sample of 27 observations from a population and wished to calculate a 90% confidence interval for the mean, µ, in the case where the population standard deviation, σ, is unknown. Enter the value from the Student's t distribution that we would use, to three decimal places.
Solutions
orchestra answered 2 years agoRelated Solutions
A random sample of 27 observations is used to estimate the population mean. The sample mean...
A random sample of 27 observations is used to estimate the
population mean. The sample mean and the sample standard deviation
are calculated as 113.9 and 20.40, respectively. Assume that the
population is normally distributed. [You may find it useful
to reference the t table.]
a. Construct the 90% confidence interval for the
population mean. (Round intermediate calculations to at
least 4 decimal places. Round "t" value to 3 decimal
places and final answers to 2 decimal places.)
b. Construct...
A random sample of 27 observations is used to estimate the population variance. The sample mean...
A random sample of 27 observations is used to estimate the
population variance. The sample mean and sample standard deviation
are calculated as 44 and 4.5, respectively. Assume that the
population is normally distributed. (You may find it useful to
reference the appropriate table: chi-square table or F table)
a. Construct the 95% interval estimate for the population
variance. (Round intermediate calculations to at least 4 decimal
places and final answers to 2 decimal places.)
b. Construct the 99% interval...
Suppose a random sample of n = 5 observations is selected from a population that is...
Suppose a random sample of n = 5 observations is selected from a
population that is normally distributed, with mean equal to 7 and
standard deviation equal to 0.33. (a) Give the mean and standard
deviation of the sampling distribution of x. (Round your standard
deviation to four decimal places.) mean standard deviation (b) Find
the probability that x exceeds 7.3. (Round your answer to four
decimal places.) (c) Find the probability that the sample mean x is
less than...
Suppose a random sample of n = 16 observations is selected from a population that is...
Suppose a random sample of n = 16 observations is selected from
a population that is normally distributed with mean equal to 105
and standard deviation equal to 11. (use SALT)
(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 109. (Round your
answer to four decimal places.)
(c) Find the probability that the sample mean deviates from the
population mean μ...
Suppose a random sample of n = 5 observations is selected from a population that is...
Suppose a random sample of n = 5 observations
is selected from a population that is normally distributed, with
mean equal to 3 and standard deviation equal to 0.35.
(a)
Give the mean and standard deviation of the sampling
distribution of x. (Round your standard deviation to four
decimal places.)
(b)
Find the probability that x exceeds 3.3. (Round your
answer to four decimal places.)
(c)
Find the probability that the sample mean x is less
than 2.5. (Round your...
The sample variance of a random sample of 50 observations from a normal population was found...
The sample variance of a random sample of 50 observations from
a normal population was found to be s2 = 80. Can we
infer at the 1% significance level (i.e., a = .01) that the
population variance is less than 100 (i.e., x < 100) ?
Repeat part a changing the sample size to 100
What is the affect of increasing the sample size?
1. Suppose we are about to sample 100 observations from a normally distributed population where it...
1. Suppose we are about to sample 100 observations from a
normally distributed population where it is known that σ = 20, but
µ is unknown. We intend to test H0: µ = 30 against Ha: µ < 30 at
α = 0.05.
(a) What values of the sample mean would lead to a rejection of
the null hypothesis?
(b) What is the power of the test if µ = 28?
(c) What is the power of the test if...
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...
A simple random sample of 25 observations will be taken from a population that is assumed...
A simple random sample of 25 observations will be taken from a
population that is assumed to be normal with a standard deviation
of 37. We would like to test the alternative hypothesis that the
standard deviation is actually more than 37. If the sample standard
deviation is 40 or more, then the null hypothesis will be rejected
(this called a decision rule).
What significance level would this decision rule cause?
If the population standard deviation is really 42, what...
A random sample of 120 observations produced a mean of ?⎯⎯⎯ =29.4 from a population with...
A random sample of 120 observations produced a mean of ?⎯⎯⎯
=29.4 from a population with a normal distribution and a standard
deviation ?=2.45.
(a) Find a 95% confidence interval for ?
___ ≤ ? ≤ ___
(b) Find a 90% confidence interval for ?
___ ≤ ? ≤ ___
(c) Find a 99% confidence interval for ?μ
___ ≤ ? ≤ ___
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