Answer all the problems. You might use illustrations and diagrams to enhance explanations.
problem1) In the study on a cost living index for the particular year in the city, following weekly observations were made.
Cost of living index(Rs.) 140-150 150-160 160-170 170-180 180-190 190-200
Number of Weeks 5 10 20 9 6 2
Draw the histogram and the frequency polygon on a same scale
problem2) The following table gives distribution of students and also regular players among them, according to age groups. Is there any correlation between ages and playing habits?
Age of groups(Years) 15-16 16-17 17-18 18-19 19-20 20-21
Number of Students 200 270 340 360 400 300
Number of Regular players 150 152 170 180 180 120
problem3) Following data are given for marks in the subject A and B in the certain examination :
SUBJECT A SUBJECT B
MEAN MARKS 36 85
STANDARD DEVIATION 11 8
Coefficient of correlation between A and B = ±0.66
i) Determine the two equations of regression
ii) find out the expected marks in A corresponding to 75 marks obtained in B.
problem4) Drilling machine bores holes with the mean deviation of 0.5230 cm and the standard deviation of 0.0032 cm. Compute 2-sigma and 3-sigma upper and lower control limits for means of samples 4 and make a control chart.
problem5) Construct 5- yearly moving averages from the following data
YEAR 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
SALE 105 107 109 112 114 116 118 121 123 124 125 127 129
problem6) In 120 throws of a single dice, following distribution of faces was observed.
FACES 1 2 3 4 5 6 TOTAL
F0 30 25 18 10 22 15 120
From the given data, verify that hypothesis “dice is biased” is acceptable or not.