Ask Your Teacher 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 (229.266, 233.002). 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.)

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

n = 5

The sample size is very small and the population standard deviation is also not known.

So, we will use t-interval for the confidence interval.

The (1 - α)% 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 t for α = 0.05 and n = 5 is:

*Use a t-table.

Compute the value of sample standard deviation as follows:

The critical value of t for α = 0.01 and n = 5 is:

*Use a t-table.

Construct the 99% confidence interval as follows:

Thus, the 99% confidence interval is (228.035, 234.233).

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9

abby has a greater debt becasue she owea 5 more then alan does