Bags of carrots are said to have a mass of $2$ kg. An inspector claims that the mean mass is not \

Question

Bags of carrots are said to have a mass of $2$ kg. An inspector claims that the mean mass is not $2$ kg. To test this claim, a random sample of $40$ bags is taken and the masses, $x$ kg, are summarised as follows. $$\sum x = 86 \qquad \sum x^2 = 199$$ Calculate unbiased estimates of the population mean and variance.[2] Test the inspector's claim at the $10$% significance level.[4] Explain what you understand by the phrase 'at the $10$% significance level' in the context of the question.[1] Bags of radishes are also said to have a mass of $2$ kg. The inspector decides to carry out a hypothesis test, at the $10$% significance level, on a random sample of $n$ bags of radishes to find out if the mean mass of bags is more than $2$ kg. He assumes that the masses of bags of radishes are normally distributed with standard deviation $0.45$ kg. It is given that the sample mean mass is $2.1$ kg. Find the set of possible values of $n$ that would lead to the conclusion that the mean mass of bags of radishes is more than $2$ kg.[4]

Accepted Answer

(a)$\bar{x}=2.15,s^2=0.362$ (d)$n \geq 34$

2024 YIJC H1 Q11

2024 YIJC H1 Q11