Question 1083726: a marketing manager wants to know if there is any difference in the proportion of consumers who like the taste of his product. he finds that 40 out of a sample of 85 consumers respond that they like the taste of his product. similarly 35 out of a second sample of 65 consumers respond that they like the taste of the product when they are administered a product of the next competing brand. based on these observations what should the marketing manager conclude at a 5% significance level
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the proportion that like the product is 40/85 = .47
the proportion that likes a competing product is 35/65 = .54
you want a two sample test of proportions.
the standard error of the test is square root of (.47*.53/85 + .54*.46/65) = .082
the z-score is (.47 - .54) / .082 = -.61
at 5% two tailed significance level, the critical z-score is plus or minus 1.96.
-.61 is well within the bounds of the critical z-score, therefore the results of the test are not significant and you can therefore not state that there is any significant difference between the proportion of people who like the product and the proportion of people who like a competing product better.
there are differing opinions and methods for dealing with two sample tests of a proportion.
the standard error of the test can be calculated using different formulas.
the following reference does that.
http://www.mathcracker.com/z-test-for-two-proportions.php
it calculates a common mean by using the formula (.47 + .53)/(85 + 65) = .5
it then uses this to calculate the standard error or the test using the following formula:
s = sqrt(.5 * .5 * (1/85 + 1/65)) = .082
the z-score is (.47 - .53) / .082 = -.73
the calculator got a z-score of -.824.
this was because it used more accurate numbers than i did.
the results, however, were the same.
the results were not statistically significant, therefore the alternate hypothesis was rejected and there was not enough evidence to conclude that there was any difference between the proportion of people who preferred the product versus the proportion of people who preferred another product.
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