Question

 A plastic Manufacturer tests the tensile strength of different type of polythene material. A sample of three measurements is taken for each material type and data in pounds per square inch are as follows: 

Type-I: 200 215 218 220

Type-II: 260 255 277 250

Type-III:245 240 270 -

Determine, if the mean tensile strength of the three different types of materials differ significantly. 

Answer 1

Carry out an ANOVA test, assuming the samples were normally distributed and the variances in the three populations were homogeneous. He selected Anova: Single Factor, then entered the data ranges, selected Grouped By: Rows and set Alpha to 0.05. He selected a suitable output option and then OK.

This returned a table of data as shown below.

The F value calculated was 16.8. This comfortably exceeds the stated critical value (Fcrit) of 4.45, and the probability of obtaining this result by chance (P-value) was calculated as 0.0013 (0.13% to three significant figures); hence we are able to reject the null hypothesis and conclude that there was a significant difference in average between the three samples, since P <0.05.