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Name 1\\
STAT 575 Homework \#0\\
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Problem from Lab\\
Part A\\

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<<1a, echo=TRUE, eval=TRUE, background="white", include=TRUE, fig=TRUE>>=
set.seed(1)
bindat <- rbinom(n=10000, size=10, prob=0.8)
par(mfrow=c(1,1))
hist(bindat, breaks=seq(2, 10, 1), freq=F)
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Part B\\

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1-pbinom(7, 10, 0.8)
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The probability that Dr. Dribble makes at least 8 out 10 free throws is 0.6778. 

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Part C\\
<<1c, echo=TRUE, eval=TRUE, background="white">>=
binom.test(15, 25, 0.4, alternative="greater")
hold <- binom.test(15, 25, 0.4, alternative="greater")
#the names command is useful!
names(hold)
hold$conf.int
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The hypothesis testing problem is \\
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$H_0: p = 0.4$ versus  $H_1: p > 0.4$\\
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With a p-value of 0.03439 we reject the null hypothesis. We conclude that there is evidence that the first serve percentage is not 0.4 in favor of the alternative. 
(This is if a tennis player actually makes 15/25 free throws.) \\
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You can also interpret the confidence interval!


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