These Ten-Year-Series (TYS) worked solutions with video explanations for 1986 A Level H2 Mathematics are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
The length of string in the balls of string made by a particular manufacturer has mean $\mu $m and variance $27.4$ m$^{2}$.
The manufacturer claims that $\mu =300$. A random sample of $100$ balls of string is taken and the sample sum (total length) is found to be $S$m.
(a)
If $S=29920$, test whether this provides significant evidence, at the $3%$ level, that the manufacturer’s claim overstates the value of $\mu $.
(a) If $S=29920$, test whether this provides significant evidence, at the $3%$ level, that the manufacturer’s claim overstates the value of $\mu $.
(b)
Find the set of values of $S$ (to one decimal place) for which the test concludes that the manufacturer’s claim overstates the value of $\mu $ at the $5%$ significance level.
(b) Find the set of values of $S$ (to one decimal place) for which the test concludes that the manufacturer’s claim overstates the value of $\mu $ at the $5%$ significance level.
State, giving a reason, whether it is necessary for the length of string in the balls of string to have a normal distribution for the test to be valid.
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