After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product. She samples 120 potential consumers and finds that 54 recognize this product. She uses this sample information to obtain a 95 percent confidence interval that goes from 0.36 to 0.54. True or False: This interval requires the assumption that the distribution of the number of people recognizing the product has a normal distribution.

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Business

Leroy Zhang

16 April, 21:55

After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product. She samples 120 potential consumers and finds that 54 recognize this product. She uses this sample information to obtain a 95 percent confidence interval that goes from 0.36 to 0.54. True or False: This interval requires the assumption that the distribution of the number of people recognizing the product has a normal distribution.

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Cheyenne Henderson · Answer 1

True

Explanation:

The experiment is meant to measure potential customers that recognize a new product. So the potential customer can recognize the product or not, and in these cases, we say the variable (the thing we are studying) has a binomial distribution. The parameters are n (120) and p (54/120 = 0.45). As n is bigger than 30, we can't use the binomial distribution, we have to approximate it by using another one, in this case, the normal distribution. This is because not only n>30 but also because p is between 0.1 and 0.9 (0.1