Moderate -0.3 This is a straightforward one-sample z-test with variance known, requiring standard hypothesis testing procedure (state hypotheses, calculate test statistic, compare to critical value). The context is clear, all values are given, and it follows a routine template with no conceptual complications or multi-step reasoning beyond the standard method.
6.
The level, in grams per millilitre, of a pollutant at different locations in a certain river is denoted by the random variable \(X\), where \(X\) has the distribution \(\mathrm { N } ( \mu , 0.0000409 )\).
In the past the value of \(\mu\) has been 0.0340 .
This year the mean level of the pollutant at 50 randomly chosen locations was found to be 0.0325 grams per millilitre.
Test, at the \(5 \%\) significance level, whether the mean level of pollutant has changed.
6.
The level, in grams per millilitre, of a pollutant at different locations in a certain river is denoted by the random variable $X$, where $X$ has the distribution $\mathrm { N } ( \mu , 0.0000409 )$.
In the past the value of $\mu$ has been 0.0340 .\\
This year the mean level of the pollutant at 50 randomly chosen locations was found to be 0.0325 grams per millilitre.
Test, at the $5 \%$ significance level, whether the mean level of pollutant has changed.\\
\hfill \mbox{\textit{SPS SPS SM Statistics 2023 Q6 [7]}}