what are the mean and standard deviation of a sampling distribution consisting of samples of size 16? these sameples were drawn from a population whose mean is 25 and who standard deviation is 5.

a. 25 and 1.25
b. 5 and 5
c. 25 and 5
d. 5 and 1.25
e. 25 and square root of 5

the standard deviations of SAT scores is 100 points. a researcher decides to take a sample of 500 students' scores to estimate the mean score of students in your state. what is the standard deviation of the sample mean?
a. 0.2
b. 4.47
c. 5
d. 100
e. can't determine without sample mean

what is the critical z-value for an 85% confidence interval?
a. .8023
b. 1.44
c. 1.04
d. need population standard deviation
e. need sample size

which of the follow isn't necessary to compute the sample size appropriate for a given confidence level and margin of error?
a. sample mean
b. populatuion standard deviation or an estimate of standard deviation
c. critcal z-value, z*
d. the margin of error m.
e. all of these values are neccessary

1. To find the mean of the sampling distribution, we know that it will be equal to the mean of the population, which is 25.

To find the standard deviation of the sampling distribution, we use the formula:
standard deviation of sampling distribution = standard deviation of population / square root of sample size

Plugging in the values, we get:
standard deviation of sampling distribution = 5 / square root of 16
standard deviation of sampling distribution = 5 / 4
standard deviation of sampling distribution = 1.25

Therefore, the mean and standard deviation of the sampling distribution are 25 and 1.25 respectively. So, answer choice (a) 25 and 1.25 is correct.

2. The standard deviation of the sample mean can be found using the formula:
standard deviation of sample mean = standard deviation of population / square root of sample size

Plugging in the values, we get:
standard deviation of sample mean = 100 / square root of 500

Calculating the value, we get:
standard deviation of sample mean ≈ 100 / 22.36 ≈ 4.47

Therefore, the standard deviation of the sample mean is approximately 4.47. So, answer choice (b) 4.47 is correct.

3. To find the critical z-value for an 85% confidence interval, we need to determine the corresponding z-value from the standard normal distribution.

Using a z-table or calculator, we find that the z-value for an 85% confidence interval is approximately 1.44. So, answer choice (b) 1.44 is correct.

4. To compute the sample size appropriate for a given confidence level and margin of error, we need the following:

- Sample mean: This is not necessary to compute the sample size, so answer choice (a) is correct.
- Population standard deviation or an estimate of standard deviation: This is necessary to calculate the sample size. So, answer choice (b) is incorrect.
- Critical z-value, z*: This is necessary to compute the sample size. So, answer choice (c) is incorrect.
- Margin of error m: This is necessary to determine the desired precision of the estimate and hence calculate the sample size. So, answer choice (d) is incorrect.

Therefore, the answer is (a) only the sample mean is not necessary to compute the sample size appropriate for a given confidence level and margin of error.

To calculate the mean and standard deviation of a sampling distribution, you need to use the following formulas:

Mean of the sampling distribution = Mean of the population = 25

Standard deviation of the sampling distribution = Standard deviation of the population / Square root of the sample size
= 5 / √16
= 5 / 4
= 1.25

So the correct answer is a. 25 and 1.25.

For the standard deviation of the sample mean, you can use the formula:

Standard deviation of the sample mean = Standard deviation of the population / Square root of the sample size
= 100 / √500
≈ 4.47

So the correct answer is b. 4.47.

To calculate the critical z-value for a given confidence interval, you need to refer to a standard normal distribution table or use a calculator.

For an 85% confidence interval, you want to find the z-value that leaves an area of 0.15 (1 - 0.85) in the tails. By looking at the standard normal distribution table or using a calculator, you can find that the critical z-value is approximately 1.04.

So the correct answer is c. 1.04.

To compute the sample size appropriate for a given confidence level and margin of error, you need all the following values:

a. Sample mean
b. Population standard deviation or an estimate of standard deviation
c. Critical z-value, z*
d. The margin of error m

Therefore, the correct answer is e. all of these values are necessary.

hi, u can solve it by this formula

S=√Σ(X-mean)
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n-1