Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2023 / Paper 1 / 9 / d

TODO: Attachment C is absent from the held release. Recover it to check any supplied critical-value table, significance convention or additional instructions. This leaf remains incomplete against that missing input. The printed summary statistics nevertheless allow the following conditional numerical answer, using a two-sided $5\%$ Student's t-test and independent observations with common variance.

Test $H_0:{\mu }_W={\mu }_S$ against $H_1:{\mu }_W\ne {\mu }_S$. The pooled sample variance isThe test statistic and statistical degrees of freedom areUsing the Student t-distribution directly gives a two-sided p-value $p\simeq 0.00250$ and a $5\%$ critical value $1.96076$. Thus reject equal seasonal means at $5\%$ and $1\%$; the winter mean is higher by $0.36$ concentration units. This does not establish a large physical effect or its cause.

The two variances are similar, and Welch's t-test gives essentially the same result: $t=3.02344$, $\nu \simeq 2958.36$, $p\simeq 0.00252$. Both calculations assume the counts represent independent observations. Serial dependence, repeated measurements and strong non-normality can invalidate nominal p-values; the summary table alone cannot diagnose them. The unequal means are a conclusion under these statistical assumptions, pending recovery of Attachment C.