Which distribution is used in developing an interval estimation when the population standard deviation is known?

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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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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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Which distribution is used to construct an interval estimate of a population standard deviation?

Which distribution is used in developing an interval estimation?

When the population standard deviation is known we perform what is called a?

What is the distribution used to estimate the interval for the population variance?