Standard +0.8 This is a two-sample t-test requiring students to formulate hypotheses for a difference claim (μ₁ - μ₂ > 15, not just μ₁ > μ₂), calculate pooled variance, compute the test statistic, and interpret at 1% significance. The non-zero difference in the null hypothesis and large sample sizes add complexity beyond standard two-sample tests, but it remains a structured application of learned procedures.
4 Holly, a horticultural researcher, believes that the mean height of stems on Tahiti daffodils exceeds that on Jetfire daffodils by more than 15 cm .
She measures the heights, \(x\) centimetres, of stems on a random sample of 65 Tahiti daffodils and finds that their mean, \(\bar { x }\), is 40.7 and that their standard deviation, \(s _ { x }\), is 3.4 .
She also measures the heights, \(y\) centimetres, of stems on a random sample of 75 Jetfire daffodils and finds that their mean, \(\bar { y }\), is 24.4 and that their standard deviation, \(s _ { y }\), is 2.8 .
Investigate, at the \(1 \%\) level of significance, Holly's belief.
4 Holly, a horticultural researcher, believes that the mean height of stems on Tahiti daffodils exceeds that on Jetfire daffodils by more than 15 cm .
She measures the heights, $x$ centimetres, of stems on a random sample of 65 Tahiti daffodils and finds that their mean, $\bar { x }$, is 40.7 and that their standard deviation, $s _ { x }$, is 3.4 .
She also measures the heights, $y$ centimetres, of stems on a random sample of 75 Jetfire daffodils and finds that their mean, $\bar { y }$, is 24.4 and that their standard deviation, $s _ { y }$, is 2.8 .
Investigate, at the $1 \%$ level of significance, Holly's belief.
\hfill \mbox{\textit{AQA S3 2009 Q4 [8]}}