A survey for brand recognition is done and it is determined that 68% of consumer

Question

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 unusual get 542 consumers who recognize the Dull Computer Company name? Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than mu - 2 or greater than mu + 20. No Yes

Explanation / Answer

We are given that,

60% of consumers have heard of Dull Computers.

800 consumers selected and it is to found that 542 of them have heard.

Here we can consider as normal approximation to binomial.

We have mean (µ) = np = 800 *0.60 = 480

Standard deviation (s) = sqrt (npq) = sqrt (800*0.60*(1-0.60)) = 13.9

Mean – 2* Standard deviation = 480 – ( 2*13.9) = 452.2 ~ 452

Mean + 2* Standard deviation = 480 + ( 2*13.9) = 507.8 ~ 508

So the interval is 452 and 508 and we find that the value of 542 falls outside this interval so the number 542 is unusual.

Answer:

Yes

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