QUESTION 3 (25 marks) (a) A dog store owner has 25 Maltese dogs for sale. The dogs come from a population whose mean weight ((1) is 3 kilograms and standard deviation (5) is 0.5 kilogram. (i) If the dog store owner randomly selects a dog from his store, weighs it, puts it back and repeats m 4 more times, what is the expected weight of the total weight (in kilogram) of the 5 dogs in the sample? (15) (ii) If the dog store owner randomly selects 5 dogs without replacement from his store and weighs them, what is the expected weight of the total weight (in kilogram) of the 5 dogs selected? (15) (iii) If the dog store owner randomly selects a dog from his store, weighs it, puts it back in store and repeats m4 more times, what is the standard error of the mean (in kilogram) of the 5 dogs in the sample? (0.2236) (iv) If the dog store owner randome selects 5 dogs without replacement from his store and weighs them, what is the standard error of the mean (in kilogram) of the 5 dogs in the sample? (0.2041) (v) How many times would the dog store owner have to randomly select a dog from the store. weighs it and put it back i_r_1_o[de_r_t_q take a sample whose standard error of the mean is no greater than 0.1 kilogram? (25) (vi) How many times would the dog store owner have to randomly select a dog without replacement from the store in_qrde_r_t_q take a sample whose standard error of the mean is no greater than 0.1 kilogram? (13) (b) An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. (i) Develop a 99% condence interval for the population mean. Interpret the result. (ii) What is the width of a 90% condence interval? (465.2763) (iii) What sample size would the economist need to use for a 95% condence interval of width not more than 100? (1,537)