Find the necessary confidence interval for a population mean μ for the following values. (Round your answers to three decimal places.) a 90% confidence interval, n = 140, x = 0.87, s2 = 0.087 to Interpret the interval that you have constructed. There is a 90% chance that an individual sample mean will fall within the interval. In repeated sampling, 10% of all intervals constructed in this manner will enclose the population mean. There is a 10% chance that an individual sample mean will fall within the interval. 90% of all values will fall within the interval. In repeated sampling, 90% of all intervals constructed in this manner will enclose the population mean.

So on this case the 90% confidence interval would be given by (0.829;0.911)    

And the best interpretation for this case is:

In repeated sampling, 90% of all intervals constructed in this manner will enclose the population mean.

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

population mean (variable of interest)

represent the sample standard deviation

n=140 represent the sample size  

Solution to the problem

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

  (1)

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.90 or 90%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,139)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 90% confidence interval would be given by (0.829;0.911)    

And the best interpretation for this case is:

In repeated sampling, 90% of all intervals constructed in this manner will enclose the population mean.