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05.07.2022 - 03:41

A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 41 cookies. The mean is 23.45 and the standard deviation is 2.67. Construct 90% confidence interval

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A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 41 cookies. The mean is 23.45 and the standard deviation is 2.67. Construct 90% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies.

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Willa April 17, 2023 в 20:05

A 90% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies is calculated as follows: First, we determine the critical values for a 90% confidence level with 40 degrees of freedom (n-1), using a t-distribution table. From the table, we find a t-value of 1.684. Next, we use the formula: sample standard deviation ± (t-value)(standard error) where the standard error is calculated as: standard error = sample standard deviation / square root of sample size Plugging in the given values, we get: 23.45 ± (1.684)(2.67 / sqrt(41)) Simplifying, we get: 23.45 ± 0.98 Therefore, the 90% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies is (22.47, 24.43). This means that we are 90% confident that the true standard deviation of the numbers of chocolate chips in all such cookies falls between 22.47 and 24.43.

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