A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be significant to get 634 consumers who recognize the Dull Computer Company name? Consider as significant any result

It would be significant

Step-by-step explanation:

Population proportion of consumers who recognize the company name = 68% = 0.68

If 634 consumers out of the 800 randomly selected consumers recognize the company name, sample proportion = 634/800 = 0.7925.

It is significant to get 634 because the sample proportion of consumers who recognize the company name is greater than the population proportion.

Given Information:

Probability = p = 68% = 0.68

Population = n = 800

Answer:

it would not be significant to get 634 consumers who might recognize the name of Dull Computer Company.

Step-by-step explanation:

We can check whether it would be significant to get 635 consumers who recognize the Dull Computer Company by finding out the mean and standard deviation.

mean = μ = np

μ = 800*0.68

μ = 544

standard deviation = σ = √np (1-p)

σ = √800*0.68 (1-0.68)

σ = 13.2 ≈ 13

we know that 99% of data fall within 3 standard deviations from the mean

μ ± 3σ = 544+3*13, 544-2*13

μ ± 3σ = 544+39, 544-39

μ ± 3σ = 583, 505

So we can say with 99% confidence that the number of consumers who can recognize the name of Dull Computer Company will be from 505 to 583 and since 583 < 634 we can conclude that it would not be significant to get 634 consumers who might recognize the name of Dull Computer Company.