Question # 1

A well-known multinational FMCG produces more than fifty products and sells them in the market. Out of fifty products one is mineral water for drinking purpose and supplies different size pack bottles in the market. Product manager observed that, during hot days the sale of water is more as compared to the normal days.He started the collection of data of weekly sale of water and the average weekly temperature.

Product manager was interested in developing a relationship between sales and temperature; therefore, he discussed and shared the following data with you.

sales

75

77

69

63

79

80

77

70

73

87

72

73

80

80

69

84

77

72

74

81

temperature

32

36

31

31

34

29

32

35

28

31

30

31

29

35

36

28

32

33

32

33

Sale is in thousand liters and temperature is in degree Celsius. Data is Normally distributed

You are required to determine the following information for some concrete decision:

a.Determine the statistical relationship between temperature and sale of water and interpret.

b.How much change in sales if the temperature increases by two degrees?

c.If for instance, the temperature becomes zero then how much sales will be?

d.How much percent variation in sales due to temperature and due to other factors?

e.Write the equation for the prediction of sales.

Question # 2

A nutritionist applies keto diet in a group of twenty individuals. He assumes that keto is designed with the idea of cutting carbohydrates from the food which impacts over the weight of individuals. For the verification of this assumption, he took a group of twenty individuals and kept them on two different diet plans (diet with and without carbohydrates) for a period of 16 weeks each. The weekly normally distributed data of their weight loss given below:

weekly loss in weight (in Kg)

With Carb

4

3.5

2

4.5

3

2.5

1.5

4.5

3

2.5

2.5

1.5

3

1.5

2

4

Without Carb

5

4

5

6

4.5

5

3

3.5

3.5

4

4.5

3

6

4

3

5

Answer the following questions:

a.Write the name of a statistical technique which is suitable for achieving the objective of nutritionists.

b.What is the average impact on the basis of given data?

c.Write the null and alternative hypothesis for the study.

d.What is the calculated value of the test statistic?

e.What is the conclusion of your study if the level of significance is 0.05?

Question # 3

During the days of coronavirus, people work most of the time from home. Many offices, schools, universities conduct their works, meetings, classes online. As a result of this new normal, it is assumed that on average, utility expenses per family (electricity, water, gas etc.) increases by 40% per month. For the verification of this assumption, four months data of percentage change of utility expenses of 10 families of similar size is given below and answer the following questions, the data is normally distributed:

Percentage change of utility expenses

April

33.65

37.09

29.72

33.42

38.14

34.9

37.35

38.66

22.92

34.19

May

37.19

36.61

40.35

28.19

35.19

37.43

38.03

42.99

30.22

38.8

June

37.13

36.2

43.6

35.31

33.66

28.51

37.67

20.68

38.04

38.43

July

38.84

32.17

34.9

30.17

29.63

27.14

32.17

33.46

36.72

39.64

a.Which statistical technique(s) will be suitable for testing this assumption? (Only write the name(s) of all possible techniques)

b.Write tabulated value of test statistic at 0.05 level of significance

c.Write the null and alternative hypothesis for this test.

d.Write your final conclusion about the assumption.

e.What will be the 95% confidence interval for the average percentage change of utilityexpenses on the basis of given data.

Question # 4

French Biscuit Manufacturer (FBM), produces two types of biscuits (i) double chocolate biscuits and (ii) tea time biscuits in two separate manufacturing units. They are interested in expanding the manufacturing units (one by one) because there is a demand in the market but facing a difficulty to decide which manufacturing unit should expand first. Company officials decided that the expansion decision was based upon monthly demand.

FBM official consults you and requests to give your valuable suggestion which will be helpful for final decision. you analyzed the following normally distributed data:

Monthly Sale of Biscuits

Double Chocolate

8551

6314

5259

8138

8429

4807

8025

6845

6478

7513

9125

4894

9106

8775

10070

7845

6229

8459

10542

4196

Tea Time

10247

6601

7404

8919

9255

8404

6304

7803

11474

9131

13345

8118

6713

7439

10957

12098

9134

7535

10316

8125

Kindly provide the following information regarding your data analysis.

a.Write the null and alternative hypothesis.

b.Determine the calculated value of the test statistic with equal variances assumption.

c.Calculate the tabulated value (critical value) of the test statistic at 0.05 level of significance.

d.Develop a 95% confidence interval for the difference between the average sales of the two types of biscuits assuming that the variances are equal.

e."On average, sales of double chocolate biscuit is 500 units more than tea time biscuits".

Comments in the light of part "d" result.

Question # 5

With reference to question # 4, perform the analysis for the verification of the assumption and answer the questions given below:

a.Write the name of statistical technique used for analysis

b."For the comparing the two variances, statistician study ratio of two variances while when comparing the two means, study the difference of two mean." Give the logical reason, why we study the ratio of two variances and why not the difference of two variances.

c.Write the calculated value of test statistics

d.Write the two tabulated value of test statistics.

e.Comments about the assumption taken in question # 4, in the light of your analysis.