(a)[3]
Calculate unbiased estimates for the population mean and variance.
(b)[5]
Test the passenger’s belief using the $5\%$ significance level.
Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
The random variable $T$, measured in minutes, for a particular daily bus trip is normally distributed. The bus company says that the mean value of $T$ is $45$. One passenger thinks that the true mean of $T$ exceeds $45$. She records the journey times on a random sample of $60$ days. The information is summarised below: $n = 60$, $\sum t = 2750$, $\sum t^2 = 127000$.