8 A certain species of plant produces flowers which are either red, white or pink. It...

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8 A certain species of plant produces flowers which are either red, white or pink. It also produces leaves which may be either plain or variegated. For a sample of 500 plants, the distribution of flower colour and leaf type was: de (i) le (iii) Plain Variegated (ii) Plain Variegated Red 97 105 Test whether these results indicate any association between flower colour and leaf type. A genetic model suggests that the proportions of each combination should be as follows: Red 9 9 Comment briefly on your conclusions. (a) where q (0<q<1/5) is an unknown parameter. (a) (b) No. of houses burgled x No. of streets f (b) (c) White 42 148 9 A particular area in a town suffers a high burglary rate. A sample of 100 streets is taken, and in each of the sampled streets, a sample of six similar houses is taken. The table below shows the number of sampled houses, which have had burglaries during the last six months. White 9/2 3q/2 0 1 39 Show that the maximum likelihood estimate for q is 0.181. Test whether this genetic model fits the data well. Pink 77 31 2 38 18 Pink (1-3q)/2 (1–54)/2 3 4 4 5 6 0 1 0 [12] [3] [Total 21] [6] State any assumptions needed to justify the use of a binomial model for the number of houses per street which have been burgled during the last six months. Derive the maximum likelihood estimator of p, the probability that a house of the type sampled has been burgled during the last six months. Determine the probabilities for the binomial model using your estimate of p, and, without doing a formal test, comment on the fit. [10] An insurance company works on the basis that the probability of a house being burgled over a six-month period is 0.18. Carry out a test to investigate whether the binomial model with this value of p provides a good fit for the data. [7] [Total 17] 8 A certain species of plant produces flowers which are either red, white or pink. It also produces leaves which may be either plain or variegated. For a sample of 500 plants, the distribution of flower colour and leaf type was: de (i) le (iii) Plain Variegated (ii) Plain Variegated Red 97 105 Test whether these results indicate any association between flower colour and leaf type. A genetic model suggests that the proportions of each combination should be as follows: Red 9 9 Comment briefly on your conclusions. (a) where q (0<q<1/5) is an unknown parameter. (a) (b) No. of houses burgled x No. of streets f (b) (c) White 42 148 9 A particular area in a town suffers a high burglary rate. A sample of 100 streets is taken, and in each of the sampled streets, a sample of six similar houses is taken. The table below shows the number of sampled houses, which have had burglaries during the last six months. White 9/2 3q/2 0 1 39 Show that the maximum likelihood estimate for q is 0.181. Test whether this genetic model fits the data well. Pink 77 31 2 38 18 Pink (1-3q)/2 (1–54)/2 3 4 4 5 6 0 1 0 [12] [3] [Total 21] [6] State any assumptions needed to justify the use of a binomial model for the number of houses per street which have been burgled during the last six months. Derive the maximum likelihood estimator of p, the probability that a house of the type sampled has been burgled during the last six months. Determine the probabilities for the binomial model using your estimate of p, and, without doing a formal test, comment on the fit. [10] An insurance company works on the basis that the probability of a house being burgled over a six-month period is 0.18. Carry out a test to investigate whether the binomial model with this value of p provides a good fit for the data. [7] [Total 17]

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i To test whether there is an association between flower color and leaf type we can perform a chisquare test of independence The null hypothesis is that there is no association between the two variabl... View the full answer