A hand sanitiser company, Cleanser, claims that the mean volume of each bottle of their hand sanitis

Question

A hand sanitiser company, Cleanser, claims that the mean volume of each bottle of their hand sanitiser is $15$ ml. The consumer association took a random sample of $80$ bottles and measured the volume of each bottle. It was found that the sample mean and the sample variance were $\overline{x}$ and $2$ ml$^2$ respectively. A test was conducted at the $5\%$ level of significance to test if Cleanser has overstated the mean volume of its hand sanitiser.

Explain, in the context of the question, the meaning of a random sample.[1]
Explain, in the context of the question, the meaning of 'at the $5\%$ level of significance'.[1]
Find the unbiased estimate of the population variance.[1]

It was found that there was insufficient evidence to conclude that Cleanser had overstated the mean volume of their hand sanitiser.

By defining any parameters used and stating the hypotheses clearly, find the range of values of $\overline{x}$, correct to $2$ decimal places.[5]

Accepted Answer

(i) Each bottle had an equal chance of selection, independently of the others (ii) There is a $5\%$ probability of wrongly concluding that Cleanser overstated the mean when $\mu=15\text{ ml}$ (iii) $\dfrac{160}{79}\text{ ml}^2$ (iv) $\overline x\ge14.74\text{ ml}$

Hypothesis Testing - Significance Levels and \(p\)-Values

Hypothesis Testing - Significance Levels and \(p\)-Values

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