Course Code: MSTL-001

Assignment Code: MSTL-001/TMA/2023

Maximum Marks: 100

\section{Note:}

1. All questions are compulsory.

2. Solve the following questions in MS Excel.

3. Take the screenshots of the final output/spreadsheet.

4. Paste all screenshots in the assignment booklets with all necessary interpretation and steps.

Q 1 A cooking oil supplier distributed two types of oils, say Oil A and Oil B to a large numbers of retail stores. The supplier wants to compare the popularity of both oils. For this purpose, he selects a sample of 100 stores and tracks record of the sold oils (in litres) of each type at each store. The data are noted in the following table:

Answer the following:

i) Which type of oil has more average sales?

ii) Which oil shows greater variability in the sales?

iii) Determine the correlation between both types of oils.

iv) Compute suitable width of the class intervals for both oils,

v) Construct the continuous frequency distribution for both oils.

Q 2 The scores (out of 100) secured by 60 employees of three different departments D1, D2 and D3 who participated in a study, are presented in the following table:

i) Compute the correlation coefficient between scores of the employees working in department D1 and the joint effects of scores of the employees of departments D1 and D2.

ii) Compute the correlation coefficient between scores of the employees working in departments D1 and D2 after eliminating the linear effect of the scores of departments D3.

iii) Also represent the scores obtained by departments D1, D2 and D3 using box plot.

Q3 An experiment was conducted to compare two metals: A and B, as bonding agents for an alloy material. Components of the alloy were bonded using the metals as bonding agents, and the pressures required to break the bonds were measured. The data for the pressures required for breaking the metal are given in the following table:

If the pressure required to break both metals are normally distributed, then answers the following questions:

i) Are the variances of the distributions of the pressure of Metals A and B equal at \(5 \%\) level of significance?

ii) If yes, check whether the average pressure for Metal \(\mathrm{A}\) is more than the Metal \(\mathrm{B}\) at \(5 \%\) level of significance?

Q 4 An investigation was performed to study the impacts of different types of machines on the production of a particular variety of toys. The six machines \((\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}\) and F) are assigned at random to 36 cells of the square with the restriction that each machine is used only once by each operator and in each time-period. The following design was obtained in which 6 operators are arranged in “columns” and 6 time-periods are in “rows”:

The average production in a day is given as follows:

Assuming that the effect of each operator, time-period and machine are normally distributed with approximately equal variances, analyse the design at \(1 \%\) level of significance. Test whether the effect of the different operators, time periods and machines on the production are significant or not. If significant, do the pair-wise comparison between them.