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 (230.061, 233.807). You decide that a confidence level of 99% is more appropriate than the 95% level used. What are the limits of the 99% interval?

Answer 1

Answer:

(229.5450, 234. 3230)

Step-by-step explanation:

Given that 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.

95% confidence interval was

$(230.061, 233.807)$

From confidence interval we find mean as the average of lower and upper bound.

Mean = $\frac{463.868}{2} \\=231.934$

Margin of error = upper bound -mean

=$1.873$

i.e. 1.96 * std error = 1.873

For 99% interval margin of error would be 2.58*std error

so margin of error for 99% = $2.58*\frac{1.873}{1.96} \\=2.3890$

Confidence interval 99% lower bound = Mean - 2.3890 =229.5450

Upper bound = Mean +2.3890 = 234.3230