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A poultry farmer wants to know which breed of hen lays more eggs. A random sample...

A poultry farmer wants to know which breed of hen lays more eggs. A random sample of 60 values of the average daily egg production by the Rhode Island Red hens had a sample mean of 0.765 egg per hen and a sample standard deviation of 0.11. A random sample of 50 values of the average daily egg production by the Plymouth Rock hens had a mean of 0.559 egg per hen and a standard deviation of 0.09. Determine the degrees of freedom for a two-mean hypothesis test for population variances assumed equal (pooled estimate of the standard deviation) to test if the Rhode Island Red hens do have a greater population mean daily egg production.

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Expert Solution

Let us denote 1 by Rhode Island Red hens and Plymouth Rock by 2.

We are given that

  

Null Hypothesis:

Level of significance:

Test statistic:

Where is the pooled variance.

Critical region: .

We have

  

  

  

  

Since the calculated value of t falls in the region of rejection, we reject the null hypothesis. Hence, we conclude that there are enough evidence to claim that Rhode Island Red hens do have a greater population mean daily egg production.

orchestra answered 2 years ago
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