a)The height of students in a certain computer class is distributed with mean and standard deviation . A random sample of students was taken and the confidence interval for was found to be between cm and cm.

Estimate:

(i)Value of the sample mean;[2 Marks]

(ii)Value of .[2 Marks]

(iii) confidence interval for .[3 Marks]

b)Are professional jobs held in the computing industry independent of the number of years a person has worked in the industry? Suppose workers are interviewed. Use the results to obtained to determine whether type of professional job held in the computer industry is independent of years worked in the industry. Take .

Professional position

Years of experience

Manager

programmer

operator

Systems analysts

More than

[10 Marks]

c)Mwanga Digital Company has workers. The company is interested in knowing the average number of digital products bought per week per person by the company's workers. While the quality control manager thinks that the average number of digital products taken per worker per week is , the company secretary thinks that the true value should be more. The quality control manager subsequently selected workers at random and got the following results as digital products taken per week.

Formulatea suitable hypothesis and test it at level of significance.[8 Marks]