In a local teaching district, a technology grant is available to teachers in order to install a cluster of four computers in their classroom.

If you know the standard deviation for a population, then you can calculate a confidence interval (CI) for the mean, or average, of that population. When a statistical characteristic that’s being measured (such as income, IQ, price, height, quantity, or weight) is numerical, most people want to estimate the mean (average) value for the population. You estimate the population mean,

by using a sample mean,

plus or minus a margin of error. The result is called a confidence interval for the population mean,

When the population standard deviation is known, the formula for a confidence interval (CI) for a population mean is

deviation, n is the sample size, and z* represents the appropriate z*-value from the standard normal distribution for your desired confidence level.

The above table shows values of z* for the given confidence levels. Note that these values are taken from the standard normal (Z-) distribution. The area between each z* value and the negative of that z* value is the confidence percentage (approximately). For example, the area between z*=1.28 and z=-1.28 is approximately 0.80. Hence this chart can be expanded to other confidence percentages as well. The chart shows only the confidence percentages most commonly used.

In this case, the data either have to come from a normal distribution, or if not, then n has to be large enough (at least 30 or so) in order for the Central Limit Theorem to be applied , allowing you to use z*-values in the formula.

To calculate a CI for the population mean (average), under these conditions, do the following:

1. Determine the confidence level and find the appropriate z*-value.

   Refer to the above table.

2. Find the sample mean Quickbooks pos multi store.

   for the sample size (n).

   Note: The population standard deviation is assumed to be a known value,

3. Multiply z* times

   and divide that by the square root of n.

   This calculation gives you the margin of error.

4. Take

   plus or minus the margin of error to obtain the CI.

   The lower end of the CI is

   minus the margin of error, whereas the upper end of the CI is

   plus the margin of error.

For example, suppose you work for the Department of Natural Resources and you want to estimate, with 95% confidence, the mean (average) length of all walleye fingerlings in a fish hatchery pond.

1. Because you want a 95% confidence interval, your z*-value is 1.96.

2. Suppose you take a random sample of 100 fingerlings and determine that the average length is 7.5 inches; assume the population standard deviation is 2.3 inches. This means

3. Multiply 1.96 times 2.3 divided by the square root of 100 (which is 10). The margin of error is, therefore,

4. Your 95% confidence interval for the mean length of walleye fingerlings in this fish hatchery pond is

   (The lower end of the interval is 7.5 – 0.45 = 7.05 inches; the upper end is 7.5 + 0.45 = 7.95 inches.)

After you calculate a confidence interval, make sure you always interpret it in words a non-statistician would understand. That is, talk about the results in terms of what the person in the problem is trying to find out — statisticians call this interpreting the results “in the context of the problem.” In this example you can say: “With 95% confidence, the average length of walleye fingerlings in this entire fish hatchery pond is between 7.05 and 7.95 inches, based on my sample data.” (Always be sure to include appropriate units.)

Confidence intervals for the population mean are constructed, on the basis of not knowing the population variance. The boundaries of each 95% confidence interval are.

. Mac: Choose Minitab Express Check for Updates. PC: Choose File Help Check for Updates 2. Click Install. Note: If you are attempting to update from Minitab Express 1.1 to 1.2 or 1.3 after installing OS X Yosemite, you must open Minitab Express in unlicensed mode to apply the update.

To open Minitab Express 1.1 in unlicensed mode: 1. Open Minitab Express on the Mac. A License Utility – Find License dialog box will appear.

Click Cancel. You will receive an error message informing you that a valid license for Minitab Express was not found.

Minitab Express will now open in unlicensed mode. Choose Minitab Express Check for Updates. Click Install. If you are experiencing difficulty launching Minitab Express, please contact for assistance.

Minitab Procedure. Select Stat Regression Regression Fit Regression Model. Specify the response and the predictor(s).

Find Confidence Interval Minitab For Mac Download

The output will appear in the session window. Next, back up to the Main Menu having just run this regression:. Select Stat Regression Regression Predict. Specify the response.

Specify either the x value (' Enter individual values') or a column name (' Enter columns of values') containing multiple x values. Select Options.

Specify the Confidence level — the default is 95%. The output will appear in the session window. Example For people of the same age and gender, height is often considered a good predictor of weight.

The data set contains the heights ( ht, in cm) and weights ( wt, in kg) of a sample of 14 males between the ages of 19 and 26 years. Find a 95% prediction interval for the weight of a randomly selected male, aged 19 to 26, who is 170 centimeters tall. Find a 95% confidence interval for the average weight of all males, aged 19 to 26, who are 170 centimeters tall. Minitab dialog boxes Resulting Sample Minitab Output Video Review.