### Problem 6 The costs (in thousands of dollars) for tuition, room, and board p
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Question
### Problem 6 The costs (in thousands of dollars) for tuition, room, and board per year at 15 randomly selected public colleges and 10 randomly selected private colleges are shown in the table included below. Test the null hypothesis that the mean yearly cost at private colleges exceeds the mean yearly cost at public colleges by 10 thousand dollars versus the alternative hypothesis that the difference is not 10 thousand dollars. Use level of significance 0.05 Public Colleges: 4.2,9.1,11 . 6, 6.1,7·7,10.4,4.9,6.5,5.0,8.5,6·2,10.4,4.6,10.2,8.1 Private Colleges: 13.0,17.7,18.8,17.6,13.2,19.8,14.4,16.8,17.7,16.1 .. {r} #Include R code below this lineExplanation / Answer
> private=c(13.0,17.7,18.8,17.6,13.2,19.8,14.4,16.8,17.7,16.1)
>
> public=c(4.2,9.1,11.6,6.1,7.7,10.4,4.9,6.5,5.0,8.5,6.2,10.4,4.6,10.2,8.1)
>
> private=c(13.0,17.7,18.8,17.6,13.2,19.8,14.4,16.8,17.7,16.1)
> t.test(public, y = private,
+ alternative = "two.sided",
+ mu = 10)
Welch Two Sample t-test
data: public and private
t = -19.712, df = 20.054, p-value = 1.344e-14
alternative hypothesis: true difference in means is not equal to 10
95 percent confidence interval:
-10.947569 -6.939097
sample estimates:
mean of x mean of y
7.566667 16.510000
Comment: The estimated p-value is 1.344e-14. Hence, we can not accept the null hypothesis and conclude that the cost of tuition, room, and board per year between the public and private colleges is not 10 thousand dollars.
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