15 Bottles of Fizzipop nominally contain 330 ml of drink. A consumer affairs researcher collects a random sample of 55 bottles of Fizzipop and records the volume of drink in each bottle.
Summary statistics for the researcher's sample are shown in the table.
| \(n\) | 55 |
| \(\sum x\) | 18535 |
| \(\sum x ^ { 2 }\) | 6247066.6 |
- Calculate the mean volume of drink in a bottle of Fizzipop.
- Show that the standard deviation of the volume of drink in a bottle of Fizzipop is 3.78 ml .
The researcher uses software to produce a histogram with equal class intervals, which is shown below.
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- Explain why the researcher decides that the Normal distribution is a suitable model for the volume of drink in a bottle of Fizzipop.
- Use your answers to parts (a) and (b) to determine the expected number of bottles which contain less than 330 ml in a random sample of 100 bottles.
In order to comply with new regulations, no more than 1\% of bottles of Fizzipop should contain less than 330 ml .
The manufacturer decides to meet the new regulations by adjusting the manufacturing process so that the mean volume of drink in a bottle of Fizzipop is increased.
The standard deviation is unaltered.
- Determine the minimum mean volume of drink in a bottle of Fizzipop which should ensure that the new regulations are met. Give your answer to \(\mathbf { 3 }\) significant figures.
The mean volume of drink in a bottle of Fizzipop is set to 340 ml . After several weeks the quality control manager suspects the mean volume may have reduced. She collects a random sample of 100 bottles of Fizzipop.
The mean volume of drink in a bottle in the sample is found to be 339.37 ml .
- Assuming the standard deviation is unaltered, conduct a hypothesis test at the \(5 \%\) level to determine whether there is any evidence to suggest that the mean volume of drink in a bottle of Fizzipop is less than 340 ml .