Question

A botanist wishes to estimate the typical number of seeds for a certain fruit. She samples 36 specimens and counts the number of seeds in each. Use her sample results (mean = 58.3, standard deviation = 16.7) to find the 99% confidence interval for the number of seeds for the species. Enter your answer as an open-interval (i.e., parentheses) accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). 99% C.I. = Answer should be obtained without any preliminary rounding.

Answer 1

Solution :

The 99% confidence interval for population mean is given as follows :

Where, x̅ is sample mean, s is sample standard deviation, n is sample size and t(0.01/2, n - 1) is critical t-value to construct 99% confidence interval.

We have,  x̅ = 58.3, s = 16.7, n = 36

Using t-table we get, t(0.01/2, 36 - 1) = 2.724

Hence, 99% confidence interval for the mean number of seeds for the species is,

The 99% confidence interval for the number of seeds for the species is (50.7, 65.9).

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