Practise deriving expected frequencies, combining sparse categories and carrying out chi-squared goodness-of-fit or independence tests with justified degrees of freedom.
Apples are sold in bags of 5. Based on her previous experience, Freya claims that the probability of any apple weighing more than 100 grams is 0.35, independently of other apples in the bag.
The apples in a random sample of 150 bags are checked and the number, x, in each bag weighing more than 100 grams is recorded. The results are shown in the following table.
Carry out a goodness of fit test at the 5\% significance level and hence comment on Freya's claim.
A town council has published its plans for redeveloping the town centre and residents are being asked whether they approve or disapprove. A random sample of 250 responses has been selected from residents in the four main streets in the town: North, East, South and West Streets. The results are shown in the table.
Test, at the 5% significance level, whether the opinions of the residents are independent of the streets on which they live.
Apples are sold in bags of 5. Based on her previous experience, Freya claims that the probability of any apple weighing more than 100 grams is 0.35, independently of other apples in the bag.
The apples in a random sample of 150 bags are checked and the number, x, in each bag weighing more than 100 grams is recorded. The results are shown in the following table.
Carry out a goodness of fit test at the 5\% significance level and hence comment on Freya's claim.