Statistics Assignment: TMA Submission - Course Code, Title of TMA, SUSS PI No., Your Name, and Submi

You are to include the following particulars in your submission: Course Code, Title of the TMA, SUSS PI No., Your Name, and Submission Date.

Question 1

(a) Suppose an engineering company manufactures a critical part that has a mean diameter of 50 mm and a variance of 16 mm2. Analyse and calculate the probability that a random sample of 40 parts will have an average diameter:

(i) less than 49,

(ii) more than 51.5,

(iii) between 49 and 51. State any assumptions used.

(b) A study is conducted to examine the effects of educational level on the productivity performance level of a group of employees in a company. The data is shown in Table Q1(b) below. You are required to carry out a chi-square test to determine whether there is sufficient evidence to conclude that the operators’ educational level and productivity
performance are two independent variables.

Productivity

Performance

Educational level

‘O’ levels or lower ‘A’ levels /Poly & beyond Below average 16 14 Average 15 24 Good 19 22

Table Q1(b)

(i) State the hypotheses.

(ii) Compute the expected frequencies.

(iii) At α = 0.01, determine the value of the test statistic. Analyse the results and draw your conclusions.