n <- sample(120:250, 1) mu <- sample(c(125, 200, 250, 500, 1000), 1) y <- rnorm(n, mean = mu * runif(1, min = 0.9, max = 1.1), sd = mu * runif(1, min = 0.02, max = 0.06) ) Mean <- round(mean(y), digits = 1) Var <- round(var(y), digits = 2) tstat <- round((Mean - mu)/sqrt(Var/n), digits = 3)
A machine fills milk into r mu
ml packages. It is suspected that the
machine is not working correctly and that the amount of milk filled differs
from the setpoint $\mu_0 = r mu
$. A sample of $r n
$ packages
filled by the machine are collected. The sample mean $\bar{y}$ is equal to
$r Mean
$ and the sample variance $s^2_{n-1}$ is equal to
$r Var
$.
Test the hypothesis that the amount filled corresponds on average to the setpoint. What is the absolute value of the t-test statistic?
The t-test statistic is calculated by:
$$
\begin{aligned}
t = \frac{\bar y - \mu_0}{\sqrt{\frac{s^2_{n-1}}{n}}}
= \frac{r Mean
- r mu
}{\sqrt{\frac{r Var
}{r n
}}}
= r tstat
.
\end{aligned}
$$
The absolute value of the t-test statistic is thus equal to
r fmt(abs(tstat), 3)
.
extype: num
exsolution: r fmt(abs(tstat), 3)
exname: t statistic
extol: 0.01
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