8.29 part two Referring to the following from part one assume that 0sigma equals

Question

8.29 part two
Referring to the following from part one assume that 0sigma equals 33. How large a random sample of public owner-controlled companies is needed to make us:
a. 95% confident that Xbar, the sample mean audit delay, is within a margin of error of four days of ??mu, the true audit delay?
b. 99% confident that Xbar is within a margin of error of four days of ??mu.

from part one:
In the article Journal of management, Morris, Avila, and Allen studied innovation by surveying firms to find (among other things) the number of new products introduced by the firms.

Suppose a random sample of 100 California based firms is selected and each firm is asked to report the number of new products it has introduced during the last year. The sample mean is found to be Xbar = 5.68 assuming = 8.70:

Calculate a 98% confidence interval for the population mean number of new products introduced in the last year.

Explanation / Answer

a. ME = z* sigma/sqrt(n) for 95% confident, z* = 1.96, so: 4 = 1.96*33/sqrt(n) n = (1.96*33/4)^2 = 261 b. same but z* = 2.576, so n = (2.576*33/4)^2 = 452

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