Sem: Dec-2024 Maximum Marks: 50 Examination: End Exam Date: Duration: 2.5hrs
Programme code: 18 Programme: MBA for Working Executive	Class: FY	Semester: III Batch- 2023-24
College: K. J. Somaiya Institute of Management	Name of the department/Section/Center:
Course Code: 117P18C304	Name of the Course: Multivariate Analytics
Instructions: Attempt all the questions

Question No.	Max. Marks
1	A researcher would like to know whether gender is associated with specialization preference. The researcher collected the data and run a chi-square test. The output is mentioned below. Gender Total Male Female Specialization Preference Finance 149 148 297 Marketing 13 24 37 HR 31 37 68 Total 193 209 402 Calculated value=3.171 Degrees of freedom=2 P-value=0.205 Answer the following questions: What is the Sample Size? State the Null Hypothesis (Ho) and Alternate Hypothesis (H1). How do you get degrees of Freedom as 2? Test the Null Hypothesis at 5% level of significance? Conclude the result.	10
2	A company wants to test the lives of four types of tyres, Tyre A, Tyre B, Tyre C and Tyre D. The company collected the data on number of kilometers of each tyre used by six similar cars. The data is given below. Tyre A 33 38 36 40 31 35 Tyre B 32 40 42 38 30 34 Tyre C 31 37 35 33 34 30 Tyre D 29 34 32 30 33 31 The researcher from the company wants to determine whether there is any difference in the lives of four types of tyres. For that he run One-Way ANOVA and got the output. The output is mentioned below. ANOVA Number of kilometres Sum of Squares df Mean Square F Sig. Between Groups 77.500 3 25.833 2.388 .099 Within Groups 216.333 20 10.817 Total 293.833 23 Answer the following questions: State the Null Hypothesis (Ho) and Alternate Hypothesis (H1). How do you get degrees of Freedom for Total? How do you get degrees of Freedom for between groups? How do you get degrees of Freedom for within groups? Conclude the result at 5% level of significance.	10
3	A new fertilizer has been developed to increase the yield on crops, and the makers of the fertilizer want to better understand which of the three formulations (blends) of this fertilizer are most effective for wheat, corn, soybeans and rice (crops). They test each of the three blends on one sample of each of the four types of crops. The crop yields for the 12 combinations are as shown below. Wheat Corn Soy Rice Blend X 123 138 110 151 Blend Y 145 165 140 167 Blend Z 156 176 185 175 They run Two-Way ANOVA and get the output. The output is mentioned below. Anova: Two-Factor Without Replication SUMMARY Count Sum Average Variance Blend X 4 522 130.5 317.6667 Blend Y 4 617 154.25 188.9167 Blend Z 4 692 173 148.6667 Wheat 3 424 141.3333 282.3333 Corn 3 479 159.6667 382.3333 Soy 3 435 145 1425 Rice 3 493 164.3333 149.3333 ANOVA Source of Variation SS df MS F P-value F crit Rows 3629.167 2 1814.583 12.82643 0.006811 10.92477 Columns 1116.917 3 372.3056 2.631651 0.144561 9.779538 Error 848.8333 6 141.4722 Total 5594.917 11 Answer the following questions: State the Null Hypothesis (Ho) and Alternate Hypothesis (H1). How do you get degrees of Freedom for Rows? How do you get degrees of Freedom for columns? How do you get degrees of Freedom for Total? Conclude the result at 1% level of significance.	10
4	A researcher examined the purchasing behaviour in an online shop. The aim is to determine the influencing factors that lead a person to buy any product from the online shop after visiting the website. The online shop provides the data collected for this purpose. The researcher used logistic regression analysis to find the influencing factors. The variables used for the analysis are mentioned below. Dependent variable: Purchasing behaviour (Nominal scale) 0-Not purchasing any product 1-Purchasing any product Independent variables: Gender (Nominal scale) Age (Ratio scale) Marital status (Nominal scale) Income (Ratio scale) Time spent in the online shop (Ratio scale) Preferred mode of payment (Nominal scale) The output is given below: Variables in the Equation B S.E. Wald df Sig. Exp(B) Gender Male® Female -2.869 1.113 6.651 1 .010 .057 Age -.127 .047 7.313 1 .007 .881 Marital Status Single® Married -.782 .854 .839 1 .360 .457 Income 30000-49999® 50000-64999 .842 .985 .730 1 .393 2.321 65000 & above -.330 1.083 .093 1 .761 .719 Time spent in online shopping -.025 .020 1.636 1 .201 .975 Preferred mode of payment UPI® Credit card 1.788 .901 3.942 1 .047 5.980 Constant 5.951 1.916 9.646 1 .002 384.079 a. Variable(s) entered on step 1: Gender, Age, Marital status, Income, Time spent in online shopping, Preferred mode of payment. Note: ® refers to reference category Interpret the odds ratios. Construct the null and alternative hypothesis and conclude the result at 5% level of significance.	20