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You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:

45.9, 37.5, 49.9, 55.3, 46.7, 61.1, 30.3, 55.6, 23.4, 38, 44, 37.9

Find the 80% confidence interval. Enter your answer as an open interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). The answer should be obtained without any preliminary rounding.

80% C.I. =

Answer :

To estimate the mean temperature, calculate the sample mean and standard deviation, determine the critical value, calculate the margin of error, and construct the confidence interval with given sample temperatures. Therefore, the 80% confidence interval is (39.369, 47.471).

To estimate the mean temperature with a given sample, you can use the formula for the confidence interval. First, calculate the sample mean and the standard deviation. Then determine the critical value based on the desired confidence level. Finally, use these values to calculate the margin of error and construct the confidence interval.

Given the sample temperatures:

45.9, 37.5, 49.9, 55.3, 46.7, 61.1, 30.3, 55.6, 23.4, 38, 44, and 37.9,

the sample mean is 43.42 and the standard deviation is 11.76.

With an 80% confidence level, the critical value is 1.282.

Using the formula: Margin of Error = Critical Value * (Standard Deviation / sqrt(sample size)),

the margin of error is approximately 4.051.

Therefore, the 80% confidence interval is (43.42 - 4.051, 43.42 + 4.051)

= (39.369, 47.471).

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