8. (a) A researcher wishes to test the hypothesis that the mean family income in a particular area is more than N50,000 per month. The standard deviation is known to be N7,000. Data collected from 64 randomly selected families from the area gave an average income of N52, 000 State the hypotheses. 11. Carry out a test of your null hypothesis using 5% level of significance. (b) A random sample of daily profit (in N'm) is given as follows: 4, 6, 5, 7, If the population mean daily profit is N5.5 with standard deviation N4m. Test at 5 percent level of significance that the true population mean daily profit is greater than 5.59. The Table below shows the personnel manager's record of output achieved by his company in a certain year. Output(kg) 20 -24 24 - 29 30-34 35- 39 40 - 44 45 -49 50 - 54 55-59 60 -64 Frequency 2 6 10 16 20 12 6 2 Calculate the following measures for the given data: (a) The arithmetic mean (b) Standard deviation (c) Coefficient of variation of the data. Scanned by CamScanner (d) Assuming the third and fourth moments about the mean are -1.2 and 3.4 respectively determine the: (i) The skewness (ii) The kurtosis