Moderate -0.3 This is a straightforward one-tailed binomial hypothesis test with clearly stated hypotheses (p=0.4 vs p>0.4), standard significance level, and small sample size allowing direct calculation from tables. It requires only routine application of the binomial test procedure with no conceptual complications, making it slightly easier than average but still requiring proper statistical method.
4 The proportion of commuters in a town who travel to work by train is 0.4 . Following the opening of a new station car park, a random sample of 16 commuters is obtained, and 11 of these travel to work by train. Test at the \(1 \%\) significance level whether there is evidence of an increase in the proportion of commuters in this town who travel to work by train.
4 The proportion of commuters in a town who travel to work by train is 0.4 . Following the opening of a new station car park, a random sample of 16 commuters is obtained, and 11 of these travel to work by train. Test at the $1 \%$ significance level whether there is evidence of an increase in the proportion of commuters in this town who travel to work by train.
\hfill \mbox{\textit{OCR S2 2010 Q4 [7]}}