Example of 1-Sample Z

A scientist for a company that manufactures processed food wants to assess the percentage of fat in the company's bottled sauce. The advertised percentage is 15%. The scientist measures the percentage of fat in 20 random samples. Previous measurements found that the population standard deviation is 2.6%.

The scientist performs a 1-sample Z-test to determine whether the fat percentage differs from 15%.

Open the sample data, FatContent.MTW.
Choose Stat > Basic Statistics > 1-Sample Z.
From the drop-down list, select One or more samples, each in a column and enter Percent Fat.
In Known standard deviation, enter 2.6.
Select Perform hypothesis test.
In Hypothesized mean, enter 15.
Click OK.

Interpret the results

The null hypothesis states that the mean of the percentage of fat equals 15%. Because the p-value is 0.012, which is less than the significance level of 0.05, the scientist rejects the null hypothesis. The results indicate that mean percentage of fat differs from 15%.

Descriptive Statistics

N	Mean	StDev	SE Mean	95% CI for μ
20	16.460	2.258	0.581	(15.321, 17.599)

Test

Null hypothesis	H₀: μ = 15
Alternative hypothesis	H₁: μ ≠ 15

Z-Value	P-Value
2.51	0.012