A sample of 87 professional working women showed that theaverage amount paid ann

Question

A sample of 87 professional working women showed that theaverage amount paid annually into a private pension fund per personwas $3,352. The population standard deviation is $1,000. A sampleof 76 professional working men showed that the average amount paidannually into a private pension fund per person was $5,727, with apopulation standard deviation of $1,700. At a 1% level ofsignificance, test to see if there is a difference in the averageamount paid into private pension funds for Women and Men.

Explanation / Answer

Women: n1=87, xbar1=3352, s1=1000 Men: n2=76, xbar2=5727, s2=1700 =0.01 The test hypothesis is Ho:1=2 Ha:1 not equal 2 The test statistic is Z=(xbar1-xbar2)/[s1^2/n1 + s2^2/n2] =(3352-5727)/sqrt(1000^2/87 + 1700^2/76) =-10.67 Given =0.01, |Z(0.005)|=2.58 (check normal table) The critical value is -2.58 and 2.58. The rejection region is Z2.58. Since Z=-10.67

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