- Camilo grows two types of apple, green apples and red apples.
The standard deviation of the weights of green apples is known to be 3.5 grams.
A random sample of 80 green apples has a mean weight of 128 grams.
- Find a 98\% confidence interval for the mean weight of the population of green apples. Show your working clearly and give the confidence interval limits to 2 decimal places.
Camilo believes that the mean weight of the population of green apples is more than 10 grams greater than the mean weight of the population of red apples.
A random sample of \(n\) red apples has a mean weight of 117 grams.
The standard deviation of the weights of the red apples is known to be 4 grams.
A test of Camilo's belief is carried out at the 5\% level of significance. - State the null and alternative hypotheses for this test.
- Find the smallest value of \(n\) for which the null hypothesis will be rejected.
- Explain the relevance of the Central Limit Theorem in parts (a) and (c).
- Given that \(n = 85\), state the conclusion of the hypothesis test.