Statistic

(a) A study was made by a university on the job preference of their graduates. One of the objective is to determine the dependencies of gender and job preferences technical and non-technical). The researcher took a random sample of 300 graduates and perform a survey on their job preference. The data have been taken and recorded as shown in Table Q4 (a). Table Q4 (a): Graduates job preference based on gender and job preferences Job Preference Technical Non-technical Gender Male 140 Female 30 50 80 (i) Calculate the expected value a and the Chi Square value b, c and d, hence complete Table Q4 (a(i)). Table Q4 (a(i)): Table of observed and expected values Observed Values, (O) Expected Values, (E) (0-E) E 140 124.6667 80 95.3333 2.4662 30 3.3333 50 34.6667 b a [7 marks) (ii) Decide whether the gender of graduates and their job preference are related at 1% significance level. (5 marks) (b) An engineer in a company are investigating the performance of their machine in the production line. He tooks a sample of three machines that have different lifespan and measure the number of error the machines record each month for five months. Table Q4 (b) represents the number of errors recorded for the three machines. Table Q4 (b): Number of errors for each machines Machine 1 Machine 2 Machine 3 11 9 12 15 10 25 31 28 38 41 99 17 40 45 22 (i) Complete the following Table Q4 (b()) below by stating the value a, b, c, and d. Table Q4 (b(i)): ANOVA Table Source of df MS F Variation SS Sprea a 2 2213.067 d b SS Error Total 2855.6 7281.733 [8 marks) Decide whether the company conclude that there is a difference in the mean number of errors recorded by the three machines at 5% level of significance. [5 marks]