Saturated fat content of cooking oil

H0 :   μ = 15%
HA :   μ > 15%

Use this diagram to illustrate how to find the p-value for testing µ when σ is unknown.

Since σ is unknown, we cannot find the distn of the sample mean, even assuming H0 — hence the pale blue question mark behind the data.

The sample mean is translated into a t-statistic on the right and the tail area from the t distn (n - 1 = 12 df) is shown and translated into a p-value.

Since the p-value is less than 0.05, there is moderately strong evidence that the mean percentage of saturated fat in the oil is more than 15%.

Select Modified data from the pop-up menu and use the slider to discuss how different values for the sample mean would affect the conclusion.

Both cholesterol and saturated fats are often avoided by people who are trying to lose weight or reduce their blood cholesterol level. Cooking oil made from soybeans has little cholesterol and has been claimed to have only 15% saturated fat.

A clinician believes that the saturated fat content is greater than 15% and randomly samples 13 bottles of soybean cooking oil for testing.

Percentage saturated fat in soybean cooking oil
15.2
12.4
15.4
13.5
15.9
17.1
16.9
14.3
19.1
18.2
15.5
16.3
20.0