A new product was test marketed in the Des Moines, Iowa, and Toledo, Ohio, metropolitan areas. Advertising in the Des Moines area was done entirely on television, while adverising in the Toledo area consisted of a mixture of television, radio, newspaper and magazine ads. Two months after the advertising campaigns commenced, surveys were taken to estimate consumer awareness of the product. In the Des Moines area, 631 out of 1,000 randomly selected consumers were aware of the product, whereas in the Toledo area 789 out of 1,000 randomly selected consumers were aware of the product.
If we let p(1), represent the true proportion of consumers in the Des Moines area who are aware of the product and p(2) be the true proportion of consumers in the Toledo area who are aware of the product, estimate the difference in the proportion of consumers n the Des Moines and Toledo areas who are aware of the product, with 98% confidence.
p1 = Proportion1, p2 = Proportion2, n1= Sample1 size, n2 = Sample2 size, p = Pooled proportion,
SE = Standard error, sqrt = Square root, ~ = …
The confidence intervals for hypothesis tests are determined. A Complete, Neat and Step-by-step Solution is provided.