Answer:
The 99% confidence interval is (228.035, 234.233).
Step-by-step explanation:
The sample size selected to compute the 95% confidence interval for the true average natural frequency (Hz) of delaminated beams of a certain type is
<em>n</em> = 5
The sample size is very small and the population standard deviation is also not known.
So, we will use <em>t</em>-interval for the confidence interval.
The (1 - <em>α</em>)% confidence interval for the true mean is:
The 95% confidence interval for the true average natural frequency (Hz) of delaminated beams of a certain type is:
(Upper limit, Lower limit) = (229.266, 233.002).
Compute the value of sample mean as follows:
The critical value of <em>t</em> for <em>α</em> = 0.05 and <em>n</em> = 5 is:
*Use a <em>t</em>-table.
Compute the value of sample standard deviation as follows:
The critical value of <em>t</em> for <em>α</em> = 0.01 and <em>n</em> = 5 is:
*Use a <em>t</em>-table.
Construct the 99% confidence interval as follows:
Thus, the 99% confidence interval is (228.035, 234.233).