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, conclude). All information is given directly with no conceptual complications, making it slightly easier than average but still requiring proper statistical methodology and interpretation.
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 2021 Q6 [7]}}