Question

Each of the following is a confidence interval for μ = true average (i.e., population mean) resonance frequency (Hz) for all tennis rackets of a certain type: (109.6, 110.4) (109.4, 110.6) 

(a) What is the value of the sample mean resonance frequency? Hz 

(b) Both intervals were calculated from the same sample data. The confidence level for one of these intervals is 90% and for the other is 99%. Which of the intervals has the 90% confidence level, and why? 

The first interval has the 90% confidence level because it is a wider interval. 

The first interval has the 90% confidence level because it is a narrower interval. 

The second interval has the 90% confidence level because it is a wider interval. 

The second interval has the 90% confidence level because it is a narrower interval. 

Answer 1

Solution:

Given: Following are two confidence intervals for mean \mu.
(109.6,110.4)

(109.4,110.6)

Part a) Sample mean response frequency= ..........?

To get sample mean, add both limits and divide it by 2.

Thus

Similarly second interval would also give same value.

Part b) One of the confidence interval has 90% confidence level and other has 99% confidence level.

If confidence level is greater then confidence interval is also wider.

Thus 90% confidence interval will have narrower interval whereas 99% confidence interval will have wider.

First confidence interval is: (109.6,110.4) which is narrower than second confidence interval : (109.4,110.6)

Thus first confidence interval has 90% confidence level.

Thus correct option is:

second option:
The first confidence interval has the 90% confidence level because it is a narrower interval.