Mathematics, 22.04.2020 04:07 amanramesh2004

5. The following sample observations on total coating layer thickness (in mm) of eight wire electrodes used for Wire electrical-discharge machining (WEDM): 21 16 29 35 42 24 24 25 Calculate a 99% CI for the variance σ 2 , and the standard deviation σ of the coating layer thickness distribution

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99% CI for the variance $\sigma^{2}$ , and the standard deviation σ of the coating layer thickness distribution is [23.275 , 477.115] and [4.824 , 21.843] respectively.

Step-by-step explanation:

We are given that the following sample observations on total coating layer thickness (in mm) of eight wire electrodes used for Wire electrical-discharge machining (WEDM) : 21, 16, 29, 35, 42, 24, 24, 25

Firstly, the pivotal quantity for 99% confidence interval for the population variance is given by;

P.Q. = $\frac{(n-1)s^{2} }{\sigma^{2} }$ ~ $\chi^{2}__n_-_1$

where, $s^{2}$ = sample variance = $\frac{\sum (X-\bar X)^{2} }{n-1}$ = 67.43

n = sample of observations = 8

$\sigma^{2}$ = population variance

Here for constructing 99% confidence interval we have used chi-square test statistics.

So, 99% confidence interval for the population variance, $\sigma^{2}$ is ;

P(0.9893 < $\chi^{2}_7$ < 20.28) = 0.99 {As the critical value of chi-square at 7

degree of freedom are 0.9893 & 20.28}

P(0.9893 < $\frac{(n-1)s^{2} }{\sigma^{2} }$ < 20.28) = 0.99

P( $\frac{0.9893 }{(n-1)s^{2} }$ < $\frac{1}{\sigma^{2} }$ < $\frac{20.28 }{(n-1)s^{2} }$ ) = 0.99

P( $\frac{(n-1)s^{2} }{20.28 }$ < $\sigma^{2}$ < $\frac{(n-1)s^{2} }{0.9893 }$ ) = 0.99

99% confidence interval for $\sigma^{2}$ = [ $\frac{(n-1)s^{2} }{20.28 }$ , $\frac{(n-1)s^{2} }{0.9893 }$ ]

= [ $\frac{7\times 67.43 }{20.28 }$ , $\frac{7\times 67.43 }{0.9893 }$ ]

= [23.275 , 477.115]

99% confidence interval for $\sigma$ = [ $\sqrt{23.275}$ , $\sqrt{477.115}$ ]

= [4.824 , 21.843]

Therefore, 99% CI for the variance $\sigma^{2}$ , and the standard deviation σ of the coating layer thickness distribution is [23.275 , 477.115] and [4.824 , 21.843] respectively.

Answer from: Quest

sas (side angle side)

aa(angle angle)

sss(side side side)

sas you have to find two sides with an angle in between

aa you find two angles because it will always add up to 180

sss find all sides

step-by-step explanation:

Answer from: Quest

Y= -2x-1 the negative in front of the 2 is because the slope is negative and the -1 is because it’s down 1 on the y axis.

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5. The following sample observations on total coating layer thickness (in mm) of eight wire electrod...