A cat food company claims that 8 out of 10 cats prefer product over the competit

Question

A cat food company claims that 8 out of 10 cats prefer product over the competition. A survey of the owners of 100 pets, revealed that only in 72 cases was the preference product of the com We have reason to believe that less than 8 out of ten cats prefer such brand? Use a significance of 0.05. A cat food company claims that 8 out of 10 cats prefer product over the competition. A survey of the owners of 100 pets, revealed that only in 72 cases was the preference product of the com We have reason to believe that less than 8 out of ten cats prefer such brand? Use a significance of 0.05.

Explanation / Answer

P = 0.8

p = 0.72

H0: P = 0.8

H1: P < 0.8

The test statistic Z = (p - P)/sqrt (P * (1 - P)/n)

= (0.72 - 0.8)/sqrt(0.8 * 0.2 * 100)

= -0.08/0.04 = -2

P-VALUE = P(Z < 2)

= 0.0228

As the p-value is less than the significance level (0.0228 < 0.05), so the null hypothesis is rejected.

So there is sufficient evidence to believe that less than 8 out of 20 cats prefer such brand.

  

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