Question

After an extensive advertising campaign, the manager of a company expects the proportion of potential customers that recognize a new product to be at least 60%. She samples 120 potential consumers from the population of 1600 potential customers, and finds that 54 recognize this product. What is the probability of getting the sample proportion that she obtained (or one that is lower) if the true population proportion is .60?

Answer 1

Answer:

0.0899

Step-by-step explanation:

Here p₀ = 0.60

n = 120

p = 54 ÷ 120 = 0.45

$\sigma=\sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.60\times0.40}{1600}}=0.0123$

Thus, P(z < $\frac{p - p_0}{\sigma}$)

P(z <  -1.3416)

Φ (z <  -1.3416) = 0.0899