A chocolate company produces chocolate bars. It is known that the mean mass of the chocolate bars is

Question

A chocolate company produces chocolate bars. It is known that the mean mass of the chocolate bars is $30$ grams. The manager decides to take a random sample of $50$ chocolate bars from those produced for quality control purposes. The masses, $x$ grams, of the random sample of $50$ chocolate bars are summarised as follows. $$\sum(x-30)=35.5 \quad \sum(x-30)^2=360.43$$ State what it means for a sample to be random in this context.[1] Test, at the $2$% level of significance, the claim that the mean mass of the chocolate bars is $30$ grams. You should state your hypotheses and define any symbols that you use.[6] State, to the nearest percent, the smallest level of significance at which the null hypothesis will be rejected using the given set of data.[1] The manager modifies the machine to improve quality. After the machine is modified, the mean mass of the chocolate bars is $\mu$ grams and the variance of the masses of the chocolate bars is $0.7$ grams${}^2$. Another random sample of $40$ chocolate bars are taken. A significance test of the null hypothesis $\mu=30$ against the alternative hypothesis $\mu>30$ is carried out at the $5$% significance level. Find the set of possible values of the sample mean that would lead to the null hypothesis being rejected.[4]

Accepted Answer

(c)smallest level of significance = 6% (d)$y=\geq 30.3$

2024 DHS H1 Q10

2024 DHS H1 Q10