Standard +0.3 This is a chi-squared test for variance (not a t-test as labeled), which is a standard S4 procedure. Students need to recognize the test type, state hypotheses correctly, calculate the test statistic using the formula χ² = (n-1)s²/σ₀², and compare to critical values. While it requires careful application of the correct test, it's a routine textbook exercise with straightforward calculations once the method is identified, making it slightly easier than average.
2. A mechanic is required to change car tyres. An inspector timed a random sample of 20 tyre changes and calculated the unbiased estimate of the population variance to be 6.25 minutes \({ } ^ { 2 }\). Test, at the \(5 \%\) significance level, whether or not the standard deviation of the population of times taken by the mechanic is greater than 2 minutes. State your hypotheses clearly.
(6)
2. A mechanic is required to change car tyres. An inspector timed a random sample of 20 tyre changes and calculated the unbiased estimate of the population variance to be 6.25 minutes ${ } ^ { 2 }$. Test, at the $5 \%$ significance level, whether or not the standard deviation of the population of times taken by the mechanic is greater than 2 minutes. State your hypotheses clearly.\\
(6)\\
\hfill \mbox{\textit{Edexcel S4 2004 Q2 [6]}}