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?
b) A telephone company wants to advertise that more than 30% of all its customers have more
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.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho: salary = $40K
Ha: it isn't
alpha=0.05 P{reject Ho|Ho true}
test stat is a t(0.975, df=19)*s/sqrt(n), t is 2.09
t=(43288-40000)/4000/sqrt(20)
=3288*sqrt(20/4000
=3.68
conclude the average salary of $40,000 is not correct.
one sample proportion
Ho: percentage is 0.30 or fewer
Ha: percentage is >0.30
reject Ho if z>1.645
p hat is 0.36
z=(0.36-0.30)/sqrt (0.3*0.7/200)
=0.06/0.0324
=1.85
reject Ho
evidence supports claim that proportion is more than 0.30
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