# Testing of Hypothesis for two sample means with Z test

Refer to “Economics of Education Review” (Vol. 21, 2002) study of the relationship between education level and earnings, Excercise 6.31 (p. 336). A National Adult Literay Survey revealed that males with a postgraduate degree had a sample mean salary of of \$61,340 (with standard error = \$2,185), while females with a postgraduate degree had a sample mean salary of \$32,227 (with a standard error = \$932), Let uM represent the population mean salary of all males with postgraduate degrees and uF represent the population mean salary of all females with postgraduate degrees.

a) Set up the null and alternative hypotheses for determining whether uM exceeds uF.

b) Calculate the test statistic for the test (part a) [Sxm-xf = The sqaure root of {Sxm (with a line and a 2 over the x) +Sxf with a line and a 2 over the x).

c) Find the rejection region for the test using ?= .01.

d) Use the results, parts b and c, to make the appropriate coclusion.

NOTE: THE PROBLEM BELOW DOES NOT NEED TO BE COMPLETED. THIS IS FOR REFERENCE ONLY.

The “Economics of Educaition Review” published a paper on the relationship between education level and earnings. The data for the research wer obtained from the National Adult Literacy Survey of over 25,000 respondents. The survey revealed that males with a postgraduate degree had a mean salary of \$61,340 (with standard error = \$2,185), while females with a postgraduate degree had a mean salary of \$32,227 (with standard error \$932).

a) The article reports a 95% confidence interval for uM, the population mean salary of all males with postgraduate degrees, is (\$57,050, \$65,631). Based on this interval, is there evidence to say that uM differs from \$60,000? Explain.

b) Use the summary information to test the hypothesis that the true mean salary of males with postgraduate degrees differes from \$60,000. Use ?= .05. (Note Sx (standard error) = s/the square root of n).

c) Explain the why the inferences in parts a and b agree.

d) The article reports that a 95% confidence interval for uF, the population mean salary for all females with postgraduate degrees is (\$30,396, \$34,058). Based on this interval, is there evidence to say that uF differs from \$33,000? Explain.

e) Use the summary information to test the hypothesis that the true mean salary of females with postgraduate degrees differs from \$33,000. Use ?= .05. (Note: sx = s/the square root of n).

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