Question 1160207: A random sample of 15 teachers from Rhode Island has an average salary of $35,270, with a standard deviation of $3256. A random sample of 30 teachers from New York has an average salary of $29,512, with a standard deviation of $1432. Is there a significant difference in teachers’ salaries between the two states? Use α=0.02. Find the 98% confidence interval for the difference of the two means.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho: mu1-mu2
Ha: they aren't equal
alpha=0.02 P{reject Ho|Ho true}
test is a t, critical value is |t|>2.575
t=diff in means/SE
=6.54
p-value 6.5 x 10^(-6)
highly significant for difference between the means. The CI shows that as well, with 98% confidence the true difference in the two means is not zero and indeed well above zero.
the half-interval is t(0.99), df=16.8 (calc)*SE
the mean difference is $5758
t=2.575
se is sqrt of s1^2/n1+s2^2/n2=880.41
product is 2267
CI is mean (+/-) that ($3491, $8025) by hand.
($3494.80, $8021.20) is 98% interval by calculator
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