QUESTION THREE (a) The owner of a recreational centre is interested in testing whether the age structure of its patrons is the similar to the age structure of the population in Ghana as a whole. The following data were collected by the owner: Age groups Under 20 20 years under 40 40 years under 60 Over 60 years Recreational centre (in %) Country percentage (%) 15 30 20 28 33 22 32 20 To conduct a goodness-of-fit test at the 5% level of significance, you are required to: (i) State the three assumptions made in conducting the chi-square. (3 marks) State appropriate null and alternative hypotheses and state the critical chi-squared value. (3 marks) (1) Calculate the chi-squared test statistic and draw an appropriate conclusion. (14 marks) Total = 20 marks QUESTION FOUR The yearly incomes received by 30 randomly selected Quantitative lecturers in some selected Universities in the Greater Accra region of Ghana (to the nearest GHC 000) are as follows: 32 20 25 26 30 40 22 25 26 30 32 48 22 25 26 30 36 52 23 26 28 30 36 60 25 26 28 32 38 61 (6 marks) (a) Find the three measures of central tendencies, [You are not required to form a frequency distribution/ (b) Calculate the measures of dispersion. (3 marks) (c) Calculate the coefficient of skewness and comment on the result. (d) Calculate 90 and 95 per cent confidence intervals for the population mean. (3 (3 marks) (8 marks)