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

answer: a

step-by-step explanation:

Answer from: Quest

spinning a 1, 2, or 3. option d.

step-by-step explanation: when spinning a number graph up to 4, and aiming for any number less than 3, that automatically eliminates the number 4. now you have two numbers to spin on that are less than 3, but the number 3 is included in this question because it's no greater of an number than itself. i hope this you : )

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