2. A pet food manufacturer runs an experiment to determine whether three brands of dog food ae equally preferred by dogs. In the experiment, 150 dogs are indi- vidually presented with three dishes of food, each containing a different brand, and their choices are noted. Tabulations show that 62 dogs go to brand A, 43 to brand B, and 45 to brand C. Is there sufficient evidence to say that dogs have preferences among the brands? Test at the 10% significance level. (A) No, with x² = 2.09, there is not sufficient evidence even at the 25% signif- icance level. (B) No, with x² = 4.36, there is not sufficient evidence at the 10% level. (C) No, with x² = 19.0, there is not sufficient evidence even at the 0.1% level. (D) Yes, with x² = 4.36, there is sufficient evidence at the 10% level. (E) Yes, with x² = 19.0, there is sufficient evidence even at the 0.1% level.

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I don't get why answer is B

2. A pet food manufacturer runs an experiment to determine whether three brands
of dog food ae equally preferred by dogs. In the experiment, 150 dogs are indi-
vidually presented with three dishes of food, each containing a different brand,
and their choices are noted. Tabulations show that 62 dogs go to brand A, 43 to
brand B, and 45 to brand C. Is there sufficient evidence to say that dogs have
preferences among the brands? Test at the 10% significance level.
(A) No, with x² = 2.09, there is not sufficient evidence even at the 25% signif-
icance level.
(B) No, with x² = 4.36, there is not sufficient evidence at the 10% level.
(C) No, with x²
(D) Yes, with x² = 4.36, there is sufficient evidence at the 10% level.
(E) Yes, with x² = 19.0, there is sufficient evidence even at the 0.1% level.
19.0, there is not sufficient evidence even at the 0.1% level.
Transcribed Image Text:2. A pet food manufacturer runs an experiment to determine whether three brands of dog food ae equally preferred by dogs. In the experiment, 150 dogs are indi- vidually presented with three dishes of food, each containing a different brand, and their choices are noted. Tabulations show that 62 dogs go to brand A, 43 to brand B, and 45 to brand C. Is there sufficient evidence to say that dogs have preferences among the brands? Test at the 10% significance level. (A) No, with x² = 2.09, there is not sufficient evidence even at the 25% signif- icance level. (B) No, with x² = 4.36, there is not sufficient evidence at the 10% level. (C) No, with x² (D) Yes, with x² = 4.36, there is sufficient evidence at the 10% level. (E) Yes, with x² = 19.0, there is sufficient evidence even at the 0.1% level. 19.0, there is not sufficient evidence even at the 0.1% level.
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