A study was conducted to determine the relationship between usage of a library and age of users. A sample of 400 was polled and the following cross-tabulation was generated. The numbers in parentheses are the observed cell sizes (Oi).

a. Complete the table.
b. Interpret the term E1 = 17.8.
c. Calculate the X2 value.
d. Is the X2 value significant? At what level? What exactly is the null hypothesis?
e. This data set proves that the usage of the library differs by age. True or false? Why?

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Age of Library Users Row Total Prop. Under 25 26.2%(21) E 17.8 32.5% (26) 25 to 45 19.5%(41) 18.1%(38) 62.4% (1 31 ) Over 45 24.5% (27) 31.8%(35) 43.6% (48) 22.3% (89) 223 Heavy Library Medium usage 41.3% (33) Light Column total Proportion 100% (80) 100% (400) 1.00 .20 1.00