7. A manufacturer produces packets of sweets. Each packet contains 25 sweets. The manufacturer claims that, on average, 40\% of the sweets in each packet are red.
A packet is selected at random.
- Using a \(1 \%\) level of significance, find the critical region for a two-tailed test that the proportion of red sweets is 0.40
You should state the probability in each tail, which should be as close as possible to 0.005
- Find the actual significance level of this test.
The manufacturer changes the production process to try to reduce the number of red sweets. She chooses 2 packets at random and finds that 8 of the sweets are red.
- Test, at the \(1 \%\) level of significance, whether or not there is evidence that the manufacturer's changes to the production process have been successful. State your hypotheses clearly.
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