Question

#1-3 points (Note if any boxes seem not applicable, leave blank.) A market researcher wishes to assess consumers preference among three different colors available on name-brand dishwashers. The following frequencies were observed from a random sample of 150 recent sales. Color White Stainless Black Total 56 31 150 Frequency 63 Test the null hypothesis that all three colors are equally popular. Test Statistic: According to your table, the P-value is bounded by: <P-value < Is there sufficient evidence to reject that the colors are e qually popular Choose one

Answer 1

The data of the three different colors available on name-brand dishwashers are given below: Color | Frequency White 63 Stainless 56 Black 31 T Total 150 The hypothesis is given as follows: The null hypothesis is H.: The colors are equally popular. The alternative hypothesis is H.: The color are not equally popular. The number of categories is k =3. The expected values are calculated as follows: 150 = 50 The observed and expected values of each category is given below: White Stainless Black Total Color Observed Total 63 56 31 O Expected E 50 50 50 150 The test statistic is calculated as follows: y? - $(0:- E) = (0,-E) (63– 50) (56 – 50), (31–50)? 505050 13262 -192 50 50 50 169 +36 +361 50 566 50 =11.32 Hence, the test statistic is x =11.32 The degrees of freedom is calculated as follows: df =k-1 = 3-1 Hence, the degrees of freedom is df = 2. The P-value is calculated as follows: P-value = P x2 >11.32) = 0.0035 Hence, P-value = 0.0035 Hence, 0.001 < P-value < 0.005 Decision rule: If P-value <a=0.05 then reject the null hypothesis. Here, P-value=0.0035<a =0.05 then reject the null hypothesis and it can be concluded that there is enough evidence that the colors are not equally popular. o g helt ned hyggelig ind i can be concluded