6. The cinema-goers were 800 people out of a sample of 1,000 pe the period of a fortnight in a town where no TV programme was available. The cinema-goers were 700 people out of a sample of 2,800 persons during a fortnight in another town where TV Programme was available. Do you think that there has been a significant decrease in proportion of cinema-goers after in proportion of cinema-goers. Use a level of 0-01.
Answers
Answer:
let us set up the hypothesis that the two towns do not differ so far as proportion of wheat consumers is concerned, i.e. HO : p1 = p2 against Ha : p1 # p2. Computing the standard error of the
difference of proportions:
n1 = 1000, p1 = 400/1000 = 0.4; n2 = 800; p2 = 400/800 = 0.5
p = (1000 x 0.4) + (800 × 0.5)/(1000 + 800) = 400 + 400/1800
simply p = (x1 + x2)/(n1 + n2) = (400 + 400)/
(1000 + 800)/1800 = 4/9
q=1-(4/9) = 5/9
p1p2 = 0.4-0.5 = -0.1
difference/S.E. = 0.1/0.024 = 4.17.
Since the difference is more than 2.58 S.E. (1% level of significance). It could not have arisen due to fluctuations of sampling. Hence the data reveal a significant difference between town A and town B so far as the proportion of wheat consumers is concerned
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