You sample a population and find that the standard deviation of the mean in your initial sample is 17. What is the minimum number of observations you need to estimate 90%, 95%, and 99% confidence intervals of the population mean with a margin of error equal to 3?

90% confidence

So the answer for this case would be n=87 rounded up to the nearest integer

95% confidence

So the answer for this case would be n=124 rounded up to the nearest integer

99% confidence

So the answer for this case would be n=214 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean for the sample  

population mean (variable of interest)

s=17 represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

  (1)

The margin of error is given by this formula:

   (2)

And on this case we have that ME =3 and we are interested in order to find the value of n, if we solve n from equation (2) we got:

  (3)

The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.05;0;1)", and we got , replacing into formula (3) we got:

So the answer for this case would be n=87 rounded up to the nearest integer

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.025;0;1)", and we got , replacing into formula (3) we got:

So the answer for this case would be n=124 rounded up to the nearest integer

The critical value for 99% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.005;0;1)", and we got , replacing into formula (3) we got:

So the answer for this case would be n=214 rounded up to the nearest integer

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb

d is the correct answer

step-by-step explanation:

x= 8 because 3x = 3 * 8, and 3*8 = 24