Answer :
The 80% confidence interval for the mean body temperature is (98.12, 98.646).
To calculate the 80% confidence interval for the mean body temperature, we follow these steps:
The sample data is given as 97.6, 97.1, 99.7, 96.9, 99.1, 99.9, 97, 98.7, 97.3, 98.2, 98.6, 98.1
From the above, the sample size (n) is 12.
Start by calculating the sample mean by dividing the sum of the samples by the number of sample
[tex]\bar x = \dfrac{97.6 + 97.1 + 99.7 + 96.9 + 99.1 + 99.9 + 97 + 98.7 + 97.3 + 98.2 + 98.6 + 98.1}{12}[/tex]
[tex]\bar x = \dfrac{1178.2}{12}[/tex]
[tex]\bar x = 98.183[/tex]
Next, we calculate the sample standard Deviation
[tex]s = \sqrt{ \dfrac{\sum(x - \bar x)\²}{n - 1}}[/tex]
[tex]s = \sqrt{\dfrac{(97.6 - 98.183)^2 + (97.1 - 98.183)^2 + (99.7 - 98.183)^2 +....+ (98.1 - 98.183)^2}{12 - 1}}[/tex]
[tex]s = \sqrt{\dfrac{11.876668}{11}[/tex]
[tex]s = \sqrt{1.07969709091[/tex]
s = 1.039
For an 80% confidence level and degrees of freedom (df = n - 1 = 11), the critical t-value (t*) is 0.876 (See attachment for table)
Calculate the Margin of Error: Margin of Error (E)
[tex]E = \dfrac{t* s}{\sqrt n}[/tex]
[tex]E = \dfrac{0.876 * 1.039}{\sqrt{12}}[/tex]
E = 0.263
To find the confidence interval, we use the following:
CI = (mean - E, mean + E).
CI = (98.383 - 0.263, 98.383 + 0.263).
CI = (98.12, 98.646).
Missing Data
97.6, 97.1, 99.7, 96.9, 99.1, 99.9, 97, 98.7, 97.3, 98.2, 98.6, 98.1
