Question

The world's smallest mammal is the bumblebee bat. Such bats are roughly the size of a large bumblebee. A random sample of 130 of these bats had an average weight of 1.7 grams with a standard deviation of 0.22 grams. Construct a 95% confidence interval estimate of their mean weight. (10)

Answer 1

We need to construct the 95% confidence interval for the population mean u. The following information is provided: Sample Mean à = 1.7 Sample Standard Deviation (s) = 0.22 Sample Size (n) = 130 The critical value for a = 0.05 and df = n − 1 = 129 degrees of freedom is te = 21-a/2;n-1 1.979. The corresponding confidence interval is computed as shown below: S s CI = X – to X X + tex Vn' + 0.22 1.979 = 1.7 0.22 1.7 + 1.979 V130 9 V130 = (1.662, 1.738) Therefore, based on the data provided, the 95% confidence interval for the population mean is 1.662 < p < 1.738, which indicates that we are 95% confident that the true population mean u is contained by the interval (1.662, 1.738).

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