A hospital introduces a new medication regimen to help patients recover from a viral infection more

Question

A hospital introduces a new medication regimen to help patients recover from a viral infection more quickly. Previously, the average recovery time was $7.2$ days. After adopting the new regimen, a random sample of $40$ patients is observed, and their recovery times, $x$, in days, are recorded. The results are summarised below. $$\sum(x - 7.2) = -42 \quad \text{and} \quad \sum(x - 7.2)^2 = 648$$ Explain whether the hospital should carry out a one-tailed test or a two-tailed test.[1] Calculate unbiased estimates of the population mean and variance of the recovery times under the new regimen.[2] Carry out an appropriate test at the $5\%$ significance level. You should state clearly the hypotheses for your test and define any parameters that you use.[4] Explain, in the context of the question, the meaning of 'at the $5\%$ significance level'.[1] Explain whether it would have been sufficient for the hospital to take a random sample of $10$ patients and record their recovery times under the new regimen in order to carry out the hypothesis test.[1] It was discovered that an intern at the hospital had made an error in recording the recovery times. A random sample of another $30$ patients was taken and their recovery times under the new regimen was taken and recorded by a senior researcher. The sample standard deviation was found to be $1.7$ days and the sample mean time was denoted by $k$. A test at the $1\%$ significance level concludes that the average recovery time did not improve from $7.2$ days. Find the set of values of $k$.[3]

Accepted Answer

(b)$\bar{x}=6.15$, $s^2= 15.5$ (f) {$k\in \mathbb{R}: k>6.47$}

2025 VJC P2 Q12

2025 VJC P2 Q12