One-Sample Z Test

Statistics > Basic Statistics > 1-Sample Z

 

Determines whether a sample from a normal distribution with known standard deviation could have a given mean.

Use One-Sample Z Test to compute a confidence interval or perform a hypothesis test of the mean when s is known. For a two-tailed one-sample Z

H0 : µ = µ0   versus   H1: µ ≠ µ0

where m is the population mean and µ0 is the hypothesized population mean.

 

Dialog box items

Samples in columns:
Choose if you have entered raw data in columns.

oSamples: Enter the columns containing the sample data.

Summarized data:
Choose if you have summary values for the sample size, mean, and standard deviation.

oSample size: Enter the value for the sample size.

oSample Mean: Enter the value for the sample mean.

Report:
The display of outputs of VisualStat.

 

Data

Data column must be numeric. You can generate a hypothesis test or confidence interval for more than one column at a time. Missing values are ignored.

 

Charts

Displays a histogram, a histogram with a normal curve, and a boxplot.

Histogram:
Choose to display a histogram for each variable

Histogram with Normal Curve:
Choose to display a histogram with a normal curve for each variable

Boxplot of data:
Choose to display a boxplot for each variable

Options: Choose the options you want.

oExclude missing values: Check to excludes rows that have missing values.

oInverted Bar: Check to reverse the axes.

 

Options

Hypothesized mean:
Enter the test mean µ0

Standard deviation:
Enter the value for the population standard deviation.

Alternative Hypothesis:
Enter Two-sided, Upper One-sided, or Lower One-sided. If you choose an One-sided hypothesis test, an upper or lower confidence bound will be constructed, respectively, rather than a confidence interval.

Confidence Level:
Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.

 

Example

This data set was collected by Bob Zarr of NIST in January, 1990 from a heat flow meter calibration and stability analysis. The response variable is a calibration factor.

The motivation for studying this data set is to illustrate a well-behaved process where the underlying assumptions hold and the process is in statistical control.

Source: http://www.itl.nist.gov/div898/handbook/eda/section4/eda4281.htm

1.Open the DataBook compare.vstz

2.Select the sheet zarr13

3.Choose the tab Statistics, the group Basic Statistics and the command 1-Sample Z

4.Select group Samples in columns

5.In Sample, select Calib.

6.Click Options page. In Hypothesized mean, enter 9.265. In Standard deviation, enter 0.02.

7.Click OK

 

Report window output

 

One-Sample Z Test

 

Test of mu = 9.265 vs not = 9.265

The assumed standard deviation = 0.02

alternative hypothesis: true mean is not equal to 9.265

 

        N    Mean   StDev  SE Mean  95% Conf Interval   z-Stat   Proba  Alt Hypothesis

Calib  195  9.2615  0.0228   0.0014   [9.2587; 9.2643]  -2.4711  0.0135          Accept

 

 

 

Interpreting the results

 

The test statistic, Z, for testing if the population mean equals 9.265 is -2.4711. The p-value, or the probability of rejecting the null hypothesis when it is true, is 0.0135. This is called the attained significance level, p-value, or attained α of the test. Because the p-value of 0.0135 is smaller than commonly chosen α-levels, there is significant evidence that μ is not equal to 9.265, so you can reject the null hypothesis in favor of μ not being 9.265.

 

 

 

See Also:


Report | Numeric Formats