# Population Means

Pearl(1968)reports lactation studies with ewes.In one of his experiments nine ewes were divided into groups of three.In group 1 the ewes and lambs were fed freely during the lactation period;in the other groups two different methods of restricting the food intake were used.He records the yields of residual milk in grams for each ewe during the fourth through tenth weeks of lactation.Analyze the data.

Please specify the model.Do the Anova.

#### Solution Preview

Please refer to the attachment.

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<br>The question here is to compare the population means of the three groups.

<br>If there is significant difference between these averages, the restriction of food intake does have effect on the ewes; if not, no significant effect.

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<br>The null hypothesis will be that all population means are equal, the alternative hypothesis is that at least one mean is different:

<br>H0: D1=D2=D3 vs.

<br>H1: at least one D is different

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<br>The grand mean of a set of samples is the total of all the data values divided by the total sample size. Dgm=241.31

<br>The total variation (not variance) is comprised the sum of the squares of the differences of each mean with the grand mean. There is the between group variation and the within group variation. The whole ...

#### Solution Summary

Pearl(1968)reports lactation studies with ewes. In one of his experiments nine ewes were divided into groups of three. In group 1 the ewes and lambs were fed freely during the lactation period;in the other groups two different methods of restricting the food intake were used. He records the yields of residual milk in grams for each ewe during the fourth through tenth weeks of lactation.Analyze the data.

Please specify the model.Do the Anova.