Answer:
The 95% confidence interval = (98.225, 98.655)
Step-by-step explanation:
The formula for Confidence Interval =
Mean ± z × standard deviation/√n
Where Mean = 98.44°F
Standard deviation = 0.30°F
n = number of samples is 10
Because our number if samples is small, we use the t score confidence interval formula
Mean ± t × standard deviation/√n
Degrees of Freedom = n - 1
= 10 - 1 = 9
We find the t score of 95% confidence interval and degrees of freedom 9
= 2.262
Hence,
Confidence interval = 98.44 ± 2.262 × 0.30/√10
= 98.44 ± 0.214592162
Confidence Interval
98.44 - 0.214592162
= 98.225407838
≈ 98.225
98.44 + 0.214592162
= 98.654592162
≈ 98.655
The 95% confidence interval = (98.225, 98.655)
