Answer the following problem

problem 1) Random sample of 1000 workers from south India shows that their mean wages are 47/- per week with standard deviation of 28/-. Random sample of 1500 workers from north India gives mean wage of 49/- per week with standard deviation of `40/-. Is any there any major difference between their mean level of wages?   

problem 2) In the given to two groups of students drawn from two normal populations, marks obtained were as follows:

Group A    18    20    36    50    49    36    34    49    41
Group B    29    28    26    35    30    44    46    -    -

Examine at 5% level, whether two populations have the same variance.

problem 3) From the following data

X    25    22    28    26    35    20    22    40    20    18
Y    18    15    20    17    22    14    16    21    15    14

a) Compute regression equation X on Y and Y on X.

b) Estimate X when Y = 20

c) Estimate Y when X=20

d) Compute Karl Pearson's coefficient of correlation

e) Check whether Regression line is a good fit.

problem 4) An index is at 100 in 1991. it rises 5% in 1992, falls 6% in 1993, falls 5% in 1994, and rises 4% in 1995 and 7% in 1996. Compute the index numbers for all these years with 1991 as base.