Question

One of the products produced by Branco Food Company is All-Bran Cereal, which competes with three other brands of similar all-bran cereals. The company's research office wants to investigate if the percentage of people who consume all-bran cereal is the same for each of these four brands. Let us denote the four brands of cereal by and . A sample of persons who consume all-bran cereal was taken, and they were asked which brand they most often consume. Of the respondents, said they usually consume Brand , consume Brand , consume Brand , and consume Brand . Does the sample provide enough evidence to reject the null hypothesis that the percentage of people who consume all-bran cereal is the same for all four brands

Answer 1

The question is incomplete. The complete question is :

One of the products produced by Branco Food Company is All-Bran Cereal, which competes with three other brands of similar all-bran cereals. The company's research office wants to investigate if the percentage of people who consume all-bran cereal is the same for each of these four brands. Let us denote the four brands of cereal by A B C and D. A sample of 900 persons who consume all-bran cereal was taken, and they were asked which brand they most often consume. Of the respondents, 201 said they usually consume Brand A, 224 consume Brand B, 299 consume Brand C, and 176 consume Brand D. Does the sample provide enough evidence to reject the null hypothesis that the percentage of people who consume all-bran cereal is the same for all four brands? Use alpha = 0.025. Find the value of the test statistic x^2. x^2 = the tolerance is +/-2% Using alpha = 0.025, can you conclude that the current percentage distribution is different from the hypothesized one? We conclude that the current percentage distribution from the hypothesized one.

Solution :

          A      B      C      D               Total

$o_i$      201   224   299  176            900

$e_i$      225  225    225  225

$X^2 =\sum \frac{(o_i-e_i)^2}{e_i} = 37.5733$

$X^2 = 9.3484$

We reject $H_0$

$\alpha = 0.025$ level

$H_0: A = B=C=D\ \ \ (1/4)$

$H_a: A,B,C,D$  are not equal.

The distribution is multinomial hypothetical distribution.