For several years now, aspirin-based products have been losing market share to s

Question

For several years now, aspirin-based products have been losing market share to substitute analgesics such as ibuprofen and acetaminophen. As a result, large companies such as Bayer, which had previously produced only aspirin-based products, are beginning to market acetaminophen-based pain relievers (Los Angeles Times, March 27, 1993). The following table gives the proportions of individuals who preferred each of the three major pain relievers for the years 1986 and 1991.

Assume that these results were obtained on the basis of two independent samples, each of size 1000.

a)   Does statistically significant evidence exist to suggest that the proportions of aspirin users differ for 1986 and 1991? Use a .05 level test.

b)   Is there sufficient evidence to indicate that ibuprofen has increased its market share between 1986 and 1991? Use alpha= .05.    

c)   Are these tests performed in (a) and (b) related? Explain.

Explanation / Answer

1.) p1 = 0.45;n1 = 1000;

p2 = 0.34;n2 = 1000;

  p = (p1 * n1 + p2 * n2) / (n1 + n2)

= 0.395

  SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

= 0.02168

z = 5.03

P(z < 5.03) = 0.999997

p-value > 0.05

Hence, there is no significant evidence exist to suggest that the proportions of aspirin users differ for 1986 and 1991

b.)

p1 = 0.14;n1 = 1000;

p2 = 0.26;n2 = 1000;

  p = (p1 * n1 + p2 * n2) / (n1 + n2)

= 0.2

  SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

= 0.01788

z = -6.7

P(z < -6.7) = 0.0.000003

p-value < 0.05

there is sufficient evidence to indicate that ibuprofen has increased its market share between 1986 and 1991

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