tstat2: 1-Sample t-Test Statistic (Single-Choice)

Exercise template for computing the t-test statistic (single-choice) from given hypothesized mean and empirical mean and variance.

Name:
tstat2
Type:
schoice
Related:
tstat
Preview:

A machine fills milk into \(500\)ml packages. It is suspected that the machine is not working correctly and that the amount of milk filled differs from the setpoint \(\mu_0 = 500\). A sample of \(247\) packages filled by the machine are collected. The sample mean \(\bar{y}\) is equal to \(521.3\) and the sample variance \(s^2_{n-1}\) is equal to \(527.08\).

Test the hypothesis that the amount filled corresponds on average to the setpoint. What is the value of the t-test statistic?

The t-test statistic is calculated by: \[ \begin{aligned} t & = & \frac{\bar y - \mu_0}{\sqrt{\frac{s^2_{n-1}}{n}}} = \frac{521.3 - 500}{\sqrt{\frac{527.08}{247}}} = 14.581. \end{aligned} \] The t-test statistic is thus equal to \(14.581\).

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A machine fills milk into \(1000\)ml packages. It is suspected that the machine is not working correctly and that the amount of milk filled differs from the setpoint \(\mu_0 = 1000\). A sample of \(244\) packages filled by the machine are collected. The sample mean \(\bar{y}\) is equal to \(945.9\) and the sample variance \(s^2_{n-1}\) is equal to \(770.7\).

Test the hypothesis that the amount filled corresponds on average to the setpoint. What is the value of the t-test statistic?

The t-test statistic is calculated by: \[ \begin{aligned} t & = & \frac{\bar y - \mu_0}{\sqrt{\frac{s^2_{n-1}}{n}}} = \frac{945.9 - 1000}{\sqrt{\frac{770.7}{244}}} = -30.44. \end{aligned} \] The t-test statistic is thus equal to \(-30.440\).

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A machine fills milk into \(250\)ml packages. It is suspected that the machine is not working correctly and that the amount of milk filled differs from the setpoint \(\mu_0 = 250\). A sample of \(247\) packages filled by the machine are collected. The sample mean \(\bar{y}\) is equal to \(245.1\) and the sample variance \(s^2_{n-1}\) is equal to \(159.93\).

Test the hypothesis that the amount filled corresponds on average to the setpoint. What is the value of the t-test statistic?

The t-test statistic is calculated by: \[ \begin{aligned} t & = & \frac{\bar y - \mu_0}{\sqrt{\frac{s^2_{n-1}}{n}}} = \frac{245.1 - 250}{\sqrt{\frac{159.93}{247}}} = -6.089. \end{aligned} \] The t-test statistic is thus equal to \(-6.089\).

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Description:
Computing the 1-sample t-test statistic from randomly-drawn hypothesized mean, sample size, and empirical mean and variance. The correct answer has to be selected from five choice items which have been added to the numeric version of the exercise linked above.
Solution feedback:
Yes
Randomization:
Random numbers
Mathematical notation:
Yes
Verbatim R input/output:
No
Images:
No
Other supplements:
No
Template:
tstat2.Rmd
tstat2.Rnw
Raw: (1 random version)
tstat2.md
tstat2.tex
PDF:
tstat2-Rmd-pdf
tstat2-Rnw-pdf
HTML:
tstat2-Rmd-html
tstat2-Rnw-html

(Note that the HTML output contains mathematical equations in MathML, rendered by MathJax using ‘mathjax = TRUE’. Instead it is also possible to use ‘converter = “pandoc-mathjax”’ so that LaTeX equations are rendered by MathJax directly.)

Demo code:

library("exams")

set.seed(403)
exams2html("tstat2.Rmd", mathjax = TRUE)
set.seed(403)
exams2pdf("tstat2.Rmd")

set.seed(403)
exams2html("tstat2.Rnw", mathjax = TRUE)
set.seed(403)
exams2pdf("tstat2.Rnw")

TEMPLATES
schoice single-choice arithmetic t statistic statistics