A random sample of n measurements was selected from a population with standard d

Question

A random sample of n measurements was selected from a population with standard deviation sigma = 19.1 and unknown mean mu. Calculate a 95 % confidence interval for mu for each of the following situations: (a) n= 40, x bar = 95.1 ______ lessthanorequalto mu lessthanorequalto ______ (b) n = 65, x bar = 95.1 ______ lessthanorequalto mu lessthanorequalto ______ (c) n = 95, x bar = 95.1 ______ lessthanorequalto mu lessthanorequalto (d) In general, we can say that for the same confidence level, increasing the sample size ______ the margin of error (width) of the confidence interval. (Enter: "DECREASES", "DOES NOT CHANGE" or "INCREASES", without the quotes.)

Explanation / Answer

(D) In general, we can say that for the same CL, increasing the sample size decreases the margin of error (ME)

A B C n 40 65 95 sigma(std. dev.) 19.1 19.1 19.1 xbar 95.1 95.1 95.1 CI 95% 95% 95% z-score for 95% CI 1.96 1.96 1.96 SE = sigma/sqrt(n) 3.01998 2.36906 1.95962 ME = z*SE 5.91915 4.64336 3.84085 Lower limit = xbar - ME 89.18085 90.45664 91.25915 Upper limit = xbar + ME 101.01915 99.74336 98.94085

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