There are six questions in this assignment, which carries 40 marks. Rest 10 marks are for viva-voce. Answer all the questions. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation. All the following questions must be performed using a statistical package. You may use any statistical package for this purpose.

Q1. Height of students of a class having 40 students was recorded. This data is given in the following table. Perform the tasks given in (i) to (iv) on the data given below using a spreadsheet package:

          (Height in cms)

147 158 157 169 146 146 172 178 161 168

146 156 152 175 148 148 179 170 156 173

169 173 176 179 169 163 173 154 165 159

170 175 152 177 155 174 151 147 161 174

(i) Find the minimum and maximum height using spreadsheet formula.

(ii) Create 8 classes with suitable class intervals and create the frequency distribution. You must use Array formula.

(iii) Find the percentage of the students whose height is less than the mean height

(iv) Draw the histogram for the data above. Also try to relate it to normal distribution curve.

Q2. Perform the following tasks using a spreadsheet (you must either enter necessary formula that are required to calculate the value or you may use spreadsheet function for the same):

(i) Find the value of t for the given value of degree of freedom and significance level (alpha):

Degree of freedom                                  Significance

20                                                        0.01

12                                                        0.05

(ii) A company manufactures bearings of diameter of size 0.5 cm. A sample of 10 such bearings were taken out of a lot consisting of 1000 bearings. The mean sample width was found to be 0.5020 cm having a standard deviation of 0.0009 cm. Assuming random sampling and a confidence level of 95%, will you accept the bearings. Justify your answer. Make suitable assumption, if any.

Q3. A Pharmaceutical Company produces a medicine involving 10 mg of a chemical. The company has four different plants to produce this medicine. Each day five samples of each plant are taken and quantity of the chemical in them is determined. The following tables lists these details:

                         The Quantity of desired Chemical (in mgs) in Medicine

                                                                                          Plant of the Company

                                             

                                                   Sample                       A               B                C              D

                                                       1                        10.01          9.98           9.99        10.09

                                                       2                        10.10          9.94           9.95        10.04

                                                       3                        10.03          9.97            9.99        10.05

                                                       4                        10.02          9.93            9.96        10.08

                                                       5                        10.04          9.95            9.97        10.02

Perform an ANOVA using any software to test (at 5% level) whether all the four plants are producing the medicine with correct amount of chemical. Justify your findings. Make suitable assumptions, if any.

Q4.

Sales of a departmental store are calculated on daily basis. The following table lists the sales data for first 15 days of the September month. Use spreadsheet software to find the moving averages for the length of 3 and 5. Also draw suitable graphs of these moving averages.

Day                                                           Sales in Thousand Rupees

1                                                                             50

2                                                                             21

3                                                                             23

4                                                                            19

5                                                                             10

6                                                                             22

7                                                                              85

8                                                                            49

9                                                                             32

10                                                                           15

11                                                                            11

12                                                                            14

13                                                                            15

14                                                                            34

15                                                                            46

 

Q5. A company packs soap solutions in sealed bottle of 2 liters. The quality of process of producing the bottles is controlled statistically. To do so four different samples are taken at different time each day having 5 samples each. Calculate the control limits for mean and range, and plot the control charts using any statistical software. Make suitable assumptions, if any.

The data is given in the following table:

Sample number of the day                                                   The volume of soap (in liters)

                     1                                                           2.02            1.99             2.01          2.09          2.08

                     2                                                           2.10             2.02             2.10          2.06         2.01

                     3                                                            2.04            2.11              2.12          1.89         1.93

                    4                                                             2.05             2.09              2.08         1.92          2.13

 

(Please take the suitable values of d2 , d3, d4 , A2 and other variables.)

Q6. An Ice cream vendor records the sale of Icecream in different months as given in the following table. Fit a trend line using any statistical software to this sales data. Make suitable assumptions

Month                                                                                                 Jan           Feb           Mar          Apr             May            Jun            July

Sales of Ice Cream (in Rupees)                                                         100            200          300         500              800            900             800