A confectionery is selling mooncakes during the Mid-Autumn Festival. The owner claims that the mean

Question

A confectionery is selling mooncakes during the Mid-Autumn Festival. The owner claims that the mean mass of the mooncakes is at least $150$ g. The distribution of the mass of a mooncake has standard deviation $6.73$ g. A customer bought a random selection of $9$ mooncakes from the confectionery with masses, in g, as follows: $145$ $148$ $153$ $156$ $141$ $151$ $143$ $157$ $138$ Test at the $10\%$ significance level whether the owner’s claim is valid. State an assumption about the population distribution of the mass of the mooncakes.[5] In a particular country, the mean working hours of teachers in schools is $60$ hours per week. After implementation of the Home-Based Learning in all schools, the Ministry claims that the mean working hours of teachers remained unchanged. A random sample of $50$ teachers was taken and the number of working hours per week was recorded. The mean working hours and standard deviation for the sample were found to be $62$ hours and $k$ hours respectively. A hypothesis test was conducted and it was found that there is sufficient evidence to reject the Ministry’s claim at $5\%$ significance level. Find the set of values of $k$.[4]

Accepted Answer

(a) From GC, ${p	ext{ }-	ext{ value} = 0.186}$ ($3$ s.f.) Since the ${p	ext{ }-	ext{ value} > 0.1}$, we do not reject ${H_0}$ and conclude that there is insufficient evidence at the ${10\%}$ significance level that the mean mass of the mooncake is less than ${150	ext{ g}}$, i.e. insufficient evidence to reject owner's claim. (b) Set of values of ${k}$ is ${\{k \in \mathbb{R} : 0 < k \leq 7.14\}}$

2022 DHS P2 Q9

2022 DHS P2 Q9

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