Each of the following is a confidence interval for u = true average(population mean) resonance frequency (Hz) for all tennis rackets of a certain type: (114.4, 115.6) (114.1, 115.9)
A) What is the value of the sample mean resonance frequency?
B) Both intervals were calculated from the same sample data. The confidence level for one of the intervals is 90% and for the other is 99%. Which of the intervals has the 90% confidence level, why?
To find the value of the sample mean resonance frequency, we need to calculate the average of the two given intervals.
A) Sample mean resonance frequency = (114.4 + 115.6) / 2 = 115 Hz
Now, let's determine which of the intervals has the 90% confidence level and why.
B) The interval with the 90% confidence level can be identified by comparing the widths of the intervals. A wider interval indicates a higher level of confidence because it allows for more variability in the population mean.
Comparing the intervals, we can see that:
Interval 1: (114.4, 115.6) has a width of 115.6 - 114.4 = 1.2 Hz.
Interval 2: (114.1, 115.9) has a width of 115.9 - 114.1 = 1.8 Hz.
Since Interval 2 has a larger width, it corresponds to a higher confidence level. Therefore, the interval (114.1, 115.9) has the 90% confidence level.
In summary, the value of the sample mean resonance frequency is 115 Hz, and the interval (114.1, 115.9) has the 90% confidence level because it has a wider width compared to the other interval.