Chapter 7 HW - 7.4 We know that is distributed as Therefore...

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HW Chp#7 7.1. (a) For N=40000, we may ignore the effect of the finite population correction factor., since it is close enough to 1(Remember, as a matter of convenience, the correction factor is usually omitted if N>20n). First, population variance is 4*= 40. For new sample variance to be equal to 1, 1= 40/should hold. Hence, the new sample is 1600 by solving this equality for n. Since N=40000 satisfies the relation, 0.05N> n, a new sample of 1600 is correct. (b) However, if N=5000, the finite population correction factor is , which may not be ignored this time. Hence, we require a smaller sample size than 1600 to reduce sample standard deviation. This can be obtained by trial and error calculations (JMP) or by analytic techniques. The new sample size should be about 1200.
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Unformatted text preview: 7.4. We know that, is distributed as . Therefore, and the value of the random variable associated with S 2 =21.96 is Therefore, Thus, the probability that when s 2 ≥21.96 is about 0.0577. (JMP) 7.25. is a random variable with 9 degrees of freedom since Z i ’s are random samples from the standard normal distribution. So P( ≤ c)=0.9=P() or 1- P()=0.1. Then using the JMP, we can calculate, so c=14.68. (JMP) 7.28. Let X i be the length of duration for each heat lamp. We want to find P(≥3100). We can use the Central Limit Theorem here because the sample size of 30 is sufficiently large. Therefore ~ N(30*100=3000, 10*sqrt(30)=54.77). So P(≥3100) = P(Z≥(3100-3000)/54.77) = P(Z≥1.83) = 1 – P(Z≤1.83) = .0336. 7.30. Since ~ , we have = = = .9947....
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