Question

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

32.1
63.7
75.9
48.6
70.6
73.8
61.5
50.2
60.1
53.8
39.9
44.1

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).

Answer 1

To find a 99% confidence interval for the mean temperature, we calculate the sample mean and standard deviation, then use these values along with the t-score for the corresponding confidence level and degrees of freedom to calculate the range.

Step-by-step explanation:

To estimate the mean temperature with a 99% confidence interval, we need to first calculate the sample mean (μ) and the sample standard deviation (s) of the given temperatures. Once we have these statistics, we can use the t-distribution as we do not know the population standard deviation and the sample size is small. The formula for the confidence interval is given by:

μ ± t*(s/√n)

where μ is the sample mean, t is the t-score from the t-distribution table corresponding to a 99% confidence level and degrees of freedom (df = n-1), s is the sample standard deviation, and n is the sample size.

Let's calculate the sample mean (average) and standard deviation using the sample temperatures:

• Average (μ) = (Sum of all temperatures) / (Number of temperatures)
• Standard Deviation (s) = √((Σ(xi - μ)²) / (n-1))

Next, we will find the t-score for a 99% confidence level with df = n - 1 degrees of freedom. With the t-score, mean, standard deviation, and sample size values, we can calculate the 99% confidence interval for the mean temperature.