In a factory, machines pack sugar into bags of $1$ kg each on average, with variance ${{\sigma }^{2}

Question

In a factory, machines pack sugar into bags of $1$ kg each on average, with variance ${{\sigma }^{2}}$kg$^{2}$. The manufacturer is concerned that the machines are putting too much sugar into the bags and decides to carry out a hypothesis test. A random sample of $8$ bags are selected and their total mass is $8.4$ kg. Stating a necessary assumption, carry out a test of the manufacturer’s concern at the $5\%$ significance level if $\sigma =0.08$. [5] Use an algebraic method to calculate the range of values of ${{\sigma }^{2}}$ for which the null hypothesis would not be rejected at the $5\%$ significance level. [3]

Accepted Answer

(i) Since $p$- value${\mathrm{= 0}\mathrm{.0385 0}\mathrm{.05}}$, we reject ${{H}_{0}}$ 	ext{ and } conclude there is sufficient evidence, at the significance $5%$ level, to support the manufacturer’s concern. (ii) ${{\sigma }^{2}}\mathrm{0}\mathrm{.007392}$

2020 RI P2 Q7

2020 RI P2 Q7

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