Question

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

56
68.6
61.5
50.5
23.5
30.9
36.6
Find the 99% 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). 99% C.I. =
Answer should be obtained without any preliminary rounding.
(a) (32.03, 57.37)
(b) (29.64, 60.76)
(c) (25.92, 64.48)
(d) (28.49, 62.91)

Answer 1

To find the 99% confidence interval for the sample temperatures, calculate the sample mean and standard deviation, then apply the t-distribution to obtain the interval.

Step-by-step explanation:

We need to estimate the mean temperature and find the 99% confidence interval for the given sample temperatures. To calculate the confidence interval, we first calculate the sample mean (μ) and the sample standard deviation (s), then use the t-distribution since we do not know the population standard deviation.

To find the 99% confidence interval, use the formula:

μ ± (t* × (s/√n))

Where μ is the sample mean, t* is the t-score corresponding to the 99% confidence level and degrees of freedom (n-1), s is the sample standard deviation, and n is the sample size.

Using the provided sample temperatures, the calculation steps would typically be:

1. Compute the sample mean.
2. Compute the sample standard deviation.
3. Determine the t-score from t-distribution tables or software.
4. Calculate the 99% confidence interval using the formula.