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29 January, 01:43

A researcher wants to see if birds that build larger nests lay larger eggs. He selects two random samples of nests: one of small nests and the other of large nests. He weighs one egg from each nest. The data are summarized below:

Small nests Large nestsSample size 60 159Sample mean (g) 37.2 35.6Sample variance 24.7 39.0Find the 95% confidence interval for the difference between the average mass of eggs in small and large nests.

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  1. 29 January, 01:49
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    95% confidence interval for the difference between the average mass of eggs in small and large nest is between a lower limit of 0.81 and an upper limit of 2.39.

    Step-by-step explanation:

    Confidence interval is given by mean + / - margin of error (E)

    Eggs from small nest

    Sample size (n1) = 60

    Mean = 37.2

    Sample variance = 24.7

    Eggs from large nest

    Sample size (n2) = 159

    Mean = 35.6

    Sample variance = 39

    Pooled variance = [ (60-1) 24.7 + (159-1) 39] : (60+159-2) = 7619.3 : 217 = 35.11

    Standard deviation = sqrt (pooled variance) = sqrt (35.11) = 5.93

    Difference in mean = 37.2 - 35.6 = 1.6

    Degree of freedom = n1+n2 - 2 = 60+159-2 = 217

    Confidence level = 95%

    Critical value (t) corresponding to 217 degrees of freedom and 95% confidence level is 1.97132

    E = t*sd/√ (n1+n2) = 1.97132*5.93/√219 = 0.79

    Lower limit = mean - E = 1.6 - 0.79 = 0.81

    Upper limit = mean + E = 1.6 + 0.79 = 2.39

    95% confidence interval for the difference in average mass is (0.81, 2.39)
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