Question

An article presents the results of a study in which the weights of 295 eggs from 27-week-old breeding hens averaged 54.1 g with a standard deviation of 4.4 g, and weights of 295 eggs from 59-week-old hens averaged 72.7 g with a standard deviation of 4.7 g. Let μX represent the population mean weight for 59-week-old hens and let μY represent the population mean weight for 27-week-old hens. Find a 95% confidence interval for the difference μX−μY . Round the answers to three decimal places. The 95% confidence interval is ( , ).

Answer 1

Solution :

The 95% confidence interval for μX − μ​​​​​​Y is given as follows:

Where, are sample means, n​​​​​​1, n​​​​​​2 are sample sizes, is the pooled estimate of common population variance and is critical t-value to construct 95% confidence interval for difference between two population means.

are sample standard deviations.

We have,

Using "tinv" function of excel we get,

Hence, 95% confidence interval for μX − μ​​​​​​Y is,

The 95% confidence interval for is (17.864 g, 19.336 g).

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