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For the interval estimation of a population mean, if the standard deviation is known and the sample size is large, the appropriate probability distribution to use is the ____. Assume that the sample size is n.A. Normal distributionB. t distribution with n degrees of freedomC. t distribution with n + 1 degrees of freedomD. t distribution with n - 1 degrees of freedom
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Video Transcript
Alright. And the given question we have been asked that for the interval estimation of population means if the population deviation is known and the sample size is large then which is what is the appropriate probability distribution to use? All right? So, here, the general rule is generally rule is if the standard deviation is unknown, then we use the T distribution right? And if the standard deviation is known, then we use the normal distribution, right? And ah since people, they often prefer to use the normal and dirty distribution, it becomes equal well into the normal when the number of cases become large. So most commonly, if the standard deviation is known, we use normal, if it is not known, and if the standard deviation is unknown, then there are two scenarios that is, if the sample size is large, then we use the normal distribution rate and if the sample size is small, then we use the T distribution Now. In this case, in the given case the population is large and the standard deviation is known to hear. The answer is obviously the normal distribution. Right? So that will be the answer for the given question. If this helps you, thank you for watching
for the interval estimation of m when s is known and the sample is large, the proper distribution to use is
the normal distribution
the t distribution with n degrees of freedom
the t distribution with n + 1 degrees of freedom
the t distribution with n + 2 degrees of freedom
QUESTION 4
The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the
confidence level
margin of error
parameter estimate
interval estimate
1 points
QUESTION 5
Whenever the population standard deviation is unknown and the population has a normal or near-normal distribution, which distribution is used in developing an interval estimation?
standard distribution
z distribution
alpha distribution
t distribution
1 points
QUESTION 6
In interval estimation, the t distribution is applicable only when
the population has a mean of less than 30
the sample standard deviation is used to estimate the population standard deviation
the variance of the population is known
the standard deviation of the population is known
1 points
QUESTION 7
In developing an interval estimate, if the population standard deviation is unknown
it is impossible to develop an interval estimate
the standard deviation is arrived at using the range
the sample standard deviation can be used
it is assumed that the population standard deviation is 1
1 points
QUESTION 8
In order to use the normal distribution for interval estimation of m when s is known and the sample is very small, the population
must be very large
must have a normal distribution
can have any distribution
must have a mean of at least 1
1 points
QUESTION 9
From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of m, the proper distribution to use is the
normal distribution
t distribution with 25 degrees of freedom
t distribution with 26 degrees of freedom
t distribution with 24 degrees of freedom
1 points
QUESTION 10
A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to 0.90, the interval for m
becomes narrower
becomes wider
does not change
becomes 0.1
1 points
QUESTION 11
After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?
Increase the level of confidence for the interval.
Decrease the sample size.
Increase the sample size.
Reduce the population variance.
1 points
QUESTION 12
An interval estimate is a range of values used to estimate
the shape of the population's distribution
the sampling distribution
a sample statistic
a population parameter
1 points
QUESTION 13
As the sample size increases, the margin of error
increases
decreases
stays the same
increases or decreases depending on the size of the mean
1 points
QUESTION 14
From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population ( m).
The normal distribution can be used.
The t distribution with 5 degrees of freedom must be used.
The t distribution with 6 degrees of freedom must be used.
The sample size must be increased.
1 points
QUESTION 15
If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect
the size of the confidence interval to increase
the size of the confidence interval to decrease
the size of the confidence interval to remain the same
the sample size to increase
1 points
QUESTION 16
If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is
0.485
1.96
0.95
1.645
1 points
QUESTION 17
In determining the sample size necessary to estimate a population proportion, which of the following information is not needed?
the maximum margin of error that can be tolerated
the confidence level required
a preliminary estimate of the true population proportion P
the mean of the population
1 points
QUESTION 18
In general, higher confidence levels provide
wider confidence intervals
narrower confidence intervals
a smaller standard error
unbiased estimates
1 points
QUESTION 19
In order to determine an interval for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is
22
23
60
61
1 points
QUESTION 20
The ability of an interval estimate to contain the value of the population parameter is described by the
confidence level
degrees of freedom
precise value of the population mean m
degrees of freedom minus 1
1 points
QUESTION 21
Using an a = 0.04 a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion
becomes narrower
becomes wider
does not change
remains the same
1 points
QUESTION 22
When constructing a confidence interval for the population mean and the standard deviation of the sample is used, the degrees of freedom for the t distribution equals
n-1
n
29
30
1 points
QUESTION 23
Whenever using the t distribution for interval estimation with a very small sample, we must assume that
the sample has a mean of at least 30
the sampling distribution is not normal
the population is approximately normal
the finite population correction factor is necessary
Answer & Explanation
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