Inference for the Mean(σKnown)
Confidence Interval
Excel does not have a routine for reporting the lower and upper limits of a confidence interval for the mean. However, you can use Excel to compute the margin of error, which can then be subtracted and added to the sample mean to get the confidence interval.
Tests of Statistical Significance
To conduct a test of the mean with known population standard deviation, Excel only provides a statistical function that will report the P-value for a one-sided, greater-than alternative hypothesis, and only with data.
Note: If your alternative hypothesis is a less-than alternative, subtract the reported P-value from 1 to obtain the appropriate P-value. For a two-sided alternative, if the reported P-value is less than 0.5, you should double it; otherwise, you should double (1 − reported P-value).
The Excel Video Technology Manuals on Confidence Intervals: Z - with Data, Confidence Intervals: Z - Summarized Data, One Mean Test: Z - with Data and Sample Size Computation can help here with additional explanation and worked examples.
Confidence Interval
With Raw Data:
With Summarized Data:
Note: A Z-Based Confidence Interval can also be obtained from Analyze ➔ Distribution. With the red arrow option choose “Confidence Interval” then “Other” then Use known sigma.
Tests of Statistical Significance
With Raw Data:
Note: You can check the box for “reveal decision” to show the conclusion of the hypothesis test.
In addition, hypothesis tests for one sample mean may be computed in a more customary way using the distribution platform:
With Summarized Data:
The JMP Video Technology Manuals on Confidence Intervals: Z - with Data, Confidence Intervals: Z - Summarized Data, One Mean Test: Z - with Data, One Mean Test: Z - Summarized Data and Sample Size Computation can help here with additional explanation and worked examples.
Both confidence intervals and hypothesis tests are done through the Stat ➔ Basic Statistics ➔ 1-Sample Z dialog.
Sample Size Needed for a Given Margin of Error
The Minitab Video Technology Manuals on Confidence Intervals: Z - with Data, Confidence Intervals: Z - Summarized Data, One Mean Test: Z - with Data, One Mean Test: Z - Summarized Data and Sample Size Computation can help here with additional explanation and worked examples.
SPSS does not compute confidence intervals, hypothesis tests, or power for one mean when sigma is known.
Note: See the SPSS technology manual for this chapter for instructions on using SPSS as a calculator to perform the tests and procedures above.
Both confidence intervals and hypothesis tests are done through the Statistics ➔ Z ➔ 1-Sample dialog.
The CrunchIt! Help Videos on Confidence Intervals Using Z, One Mean Test Using Z, and Sample Size Computation for One Mean Inference Using Z can help here with examples.
R does not have automatic routines to compute confidence intervals, hypothesis tests, or power for one mean when sigma is known. You can use pnorm(z) to find P(Z<z) for the P-value of a test or the power of a test as described in the text.
The R Video Technology Manuals on Confidence Intervals for a Population Mean Based on Z, Significance Test for a Population Mean Based on Z, and Sample Size Computation for Inference on a Population Mean can help here with additional explanation and worked examples.
Confidence Interval
Tests of Statistical Significance
The TI-83/-84 Video Technology Manuals on Confidence Intervals: Z - with Data, Confidence Intervals: Z - Summarized Data, One Mean Test: Z - with Data, One Mean Test: Z - Summarized Data and Sample Size Computation can help here with additional explanation and worked examples.
Power
Automated power calculations are not available in standard Excel or the enhanced add-on version of Excel. However, you can compute power in Excel by following the general steps for computing power described in this chapter and then use Excel’s NORMDIST function.
Note: Minitab assumes a two-sided alternative and 5% significance level. If you wish to have a one-sided alternative or change an α level, click “Options,” change the value, and click “OK” to return to the main dialog. Additionally, Minitab will produce a “Power Curve,” which is simply a graph of the different power values against a range of difference values.
SPSS does not compute confidence intervals, hypothesis tests, or power for one mean when sigma is known.
Note: See the SPSS technology manual for this chapter for instructions on using SPSS as a calculator to perform the tests and procedures above.
To Determine Power for a Given Sample:
To Determine Sample Size for a Desired Power:
R does not have built-in functions for this situation, but one can type R commands using it as a calculator to obtain various things like z test statistic and interval limits. You can use pnorm(z) to find P(Z≤z) for the P-value of a test or the power of a test as described in the text.
Automated power calculations are not available; however, power can be calculated by using normalCDF as described in the Chapter 1 Appendix. For more detailed instructions, see the technology manual for this chapter.