Question

A journal article reports that a sample of size 5 was used as a basis for calculating a 95% CI for the true average natural frequency (Hz) of delaminated beams of a certain type. The resulting interval was (229.964, 233.704). You decide that a confidence level of 99% is more appropriate than the 95% level used. What are the limits of the 99% interval? [Hint: Use the center of the interval and its width to determine x and s.] (Round your answers to three decimal places.)

Answer 1

Here we have

n=5

Here we need to use t critical value because it is not given that population standard deviation is known. Degree of freedom for t distribution is

df=n-1=4

The critical value for 95% CI using excel function "=TINV(0.05,4)" is 2.776.

The point estimate, that is sample mean, is

Adding these equations give

Therefore the margin of error is

The standard error is

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The critical value for 99% CI using excel function "=TINV(0.01,4)" is 4.604.

The margin of error is

The 99% confidence interval is