6 The numbers of green sweets in 200 randomly chosen packets of Frutos are summarised in the table.
| Number of green sweets | 0 | 1 | 2 | 3 | \(> 3\) |
| Number of packets | 32 | 50 | 97 | 21 | 0 |
- Calculate an unbiased estimate for the population mean of the number of green sweets in a packet of Frutos, and show that an unbiased estimate of the population variance is 0.783 correct to 3 significant figures.
The manufacturers of Frutos claim that the mean number of green sweets in a packet is 1.65 .
Anji believes that the true value of the mean, \(\mu\), is less than 1.65 . She uses the results from the 200 randomly chosen packets to test the manufacturers’ claim. - State suitable null and alternative hypotheses for the test.
\includegraphics[max width=\textwidth, alt={}, center]{7c078a14-98f9-4292-ae76-a2642238176f-08_2714_37_143_2008} - Show that the result of Anji's test is significant at the \(5 \%\) level but not at the \(1 \%\) level.
- It is given that Anji made a Type I error.
Explain how this shows that the significance level that Anji used in her test was not \(1 \%\).