Perform an analysis of variance (ANOVA) to determine if the differences in the percentage butterfat of the different breeds of cows is statistically significant.

If the p < .0001, there is a strong evidence against the equality of the means. It will be concluded that these dairy breeds differ in the mean butter fat content of their milk.

Step-by-step explanation:

Breed – Ayshire, Canadian, Guernsey, Holstein-Fresian, Jersey

Age Group – two different age class of cows (1 = younger, 2 = older)

Butterfat - percentage of butter fat found in the milk sample.

We begin our analysis by examining comparative displays for the butter fat content across the five breeds.

To do this select Fit Y by X from the Analyze menu and place the grouping variable, Breed, in the X box and place the response, Butterfat, in the Y box and click OK. The resulting plot simply shows a scatter plot of butter fat content versus breed. In many cases there will numerous data points on top of each other in such a display making the plot harder to read. To help alleviate this problem we can stagger or jitter the points a bit from vertical by selecting Jitter Points from the Display Options menu. To help visualize breed differences we could add quantile boxplots, mean diamonds, or mean with standard error bars to the graph. To do any or all of these select the appropriate options from the Display Options menu. The plot at the top of the next page has both quantile boxes and mean with error bars added.

We can clearly see the butter fat content is largest for Jersey and Guernsey cows and lowest for Holstein-Fresian. There also appears to be some difference in the variation of butter fat content as well. Analysis menu at the top of the window.

To test the null hypothesis that the butter fat content is the same for each of the breeds we can perform a one-way ANOVA test.

Assumptions for one-way ANOVA are:

1.) The samples are drawn independently or come from using a completely randomized design. Here we can assume the cows sampled from each breed were independently sampled.

2.) The variable of interest is normally distributed for each population.

3.) The population variances are equal across groups.

If any of these assumptions is violated, Welch’s ANOVA, which allows for inequality of the population variances will be used.

To conduct the one-way ANOVA test select Means, Anova/t-Test from the Oneway Analysis pull-down menu.

Normality appears to be satisfied

The equality of variance test results

Because there is a strong evidence against equality of the population variances we could use Welch’s ANOVA to test the equality of the means. This test allows for the population variances/standard deviations to differ when comparing the population means.

For Welch’s ANOVA.

If the p-value < .0001, there is a strong evidence against the equality of the means. It will be concluded that these dairy breeds differ in the mean butter fat content of their milk.

∠1 and ∠5

Step-by-step explanation:

You can see that all of the other angles are exactly 90 degrees. The remaining two are angles 1 and 5 which means that they have to be 90 degrees. Since they are together, they also look perfectly like a 90 degree angle.

Hope this helps :)