a simple random sample of 30 students was selected from a normally distributed population of high school…

a simple random sample of 30 students was selected from a normally distributed population of high school students. the following confidence intervals were calculated at 90, 95, and 99% confidence levels to estimate the average number of hours of sleep the students got each night. determine which confidence level goes with each confidence interval. between 7.3 and 8.7 hours of sleep: between 7.0 and 9.0 hours of sleep: between 7.2 and 8.8 hours of sleep: done
Answer
Answer:
Between 7.3 and 8.7 hours of sleep: 90% Between 7.0 and 9.0 hours of sleep: 99% Between 7.2 and 8.8 hours of sleep: 95%
Explanation:
Step1: Understand confidence - level relationship
As the confidence level increases, the width of the confidence interval increases.
Step2: Calculate widths of intervals
Width of 7.3 - 8.7 interval: $8.7 - 7.3=1.4$ Width of 7.0 - 9.0 interval: $9.0 - 7.0 = 2.0$ Width of 7.2 - 8.8 interval: $8.8 - 7.2=1.6$
Step3: Match intervals to confidence levels
The narrowest (1.4) is 90%, the widest (2.0) is 99%, and the middle - width (1.6) is 95%.