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) o

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?

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Amelia 2 weeks 2021-10-12T09:40:00+00:00 1 Answer 0

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    2021-10-12T09:41:48+00:00

    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

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