6. According to government regulations, X-ray machines should have an average em

Question

6. According to government regulations, X-ray machines should have an average emission of 60 milliRads with a standard deviation of 12 miliRads. Suppose a sample of 31 X-Ray emissions yields a mean of 62.3 milliRads and a standard deviation of 14 milliRads. a. Find a 99% error margin for the population mean emission b. Test whether the population mean emission is too high using -0.05 C. If we assume the -12, how large a sample must we take in order to be 90% confident of estimating the population mean emission to within 0.1 milliRAD?

Explanation / Answer

(a)
For 99% CI, z-value = 2.5758

SE = sigma/sqrt(n)
SE = 14/sqrt(31) = 2.5145

Margin of error, ME = z * SE
= 2.5758 * 2.5145
= 6.4769

(b)
Below are the null and alternate hypothesis
H0: mu = 60
H1: mu > 60

Test statistics, z = (62.3 - 60)/2.5145 = 0.9147

p-value = 0.1802

As p-value is greater than significance level of 0.05, we fail to reject the null hypothesis.

This means there are not sufficient evidence to conclude that population mean emission is too high.

(c)
ME = 0.1
For 90% CI, z = 1.65

n = (z*sigma/ME)^2 = (1.65*12/0.1)^2 = 39204

Hence sample size = 39204

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