document.write( "Question 1156893: a) The average salary of graduates entering the actuarial field is reported to be $40,000 . To test this , a statistics professor surveys 20 graduates and finds their average salary to be $43,288 with a standard deviation of $4000. Using α = 0.05, has he shown the reported salary incorrect?
\n" ); document.write( "b) A telephone company wants to advertise that more than 30% of all its customers have more
\n" ); document.write( " than two telephones. To support this ad, the company selects a sample of 200 customers and finds that 72 have more than two telephones. Does the evidence support the ad? Use 𝞪 = 0.05.
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Ho: salary = $40K
\n" ); document.write( "Ha: it isn't
\n" ); document.write( "alpha=0.05 P{reject Ho|Ho true}
\n" ); document.write( "test stat is a t(0.975, df=19)*s/sqrt(n), t is 2.09
\n" ); document.write( "t=(43288-40000)/4000/sqrt(20)
\n" ); document.write( "=3288*sqrt(20/4000
\n" ); document.write( "=3.68
\n" ); document.write( "conclude the average salary of $40,000 is not correct.\r
\n" ); document.write( "\n" ); document.write( "one sample proportion
\n" ); document.write( "Ho: percentage is 0.30 or fewer
\n" ); document.write( "Ha: percentage is >0.30
\n" ); document.write( "reject Ho if z>1.645
\n" ); document.write( "p hat is 0.36
\n" ); document.write( "z=(0.36-0.30)/sqrt (0.3*0.7/200)
\n" ); document.write( "=0.06/0.0324
\n" ); document.write( "=1.85
\n" ); document.write( "reject Ho
\n" ); document.write( "evidence supports claim that proportion is more than 0.30\r
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