Mathematics, 08.04.2020 03:35 danny223

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.)

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Answer from: genyjoannerubiera

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:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

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:

$\bar x=\frac{UL+LL}{2}=\frac{233.002+229.266}{2}=231.134$

The critical value of t for α = 0.05 and n = 5 is:

$t_{\alpha/2, (n-1)}=t_{0.05/2, (5-1)}=t_{0.025,4}=2.776$

*Use a t-table.

Compute the value of sample standard deviation as follows:

$\frac{UL-LL}{2}=t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}\\\frac{233.002-229.266}{2}=2.776\times\frac{s}{\sqrt{5}}\\s=1.505$

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

$t_{\alpha/2, (n-1)}=t_{0.01/2, (5-1)}=t_{0.005,4}=4.604$

*Use a t-table.

Construct the 99% confidence interval as follows:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}\\=231.134\pm 4.604\times \frac{1.505}{\sqrt{5}}\\=231.134\pm3.099\\=(228.035, 234.233)$

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

Answer from: Quest

{x = -1/2 , y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer: {x = -1/2 , y = -1

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.