Question

A new soft drink is being market tested. It is estimated that 60% of consumers will like

the new drink. A sample of 96 taste-tested the new drink.

(a) Determine the standard error of the proportion.

(b) What is the probability that more than 70% of consumers will indicate they like the drink?

Answer 1

Solution:

Given that,

n = 96

= 0.60

1 - = 1 - 0.60 = 0.40

So,

a ) =   = 0.60

Expected value = 0.60

= ( 1 - ) / n

=   0.60 * 0.40 / 96

= 0.05

= 0.05

Standard error = 0.05

b) P (   > 0.70 )

= 1 - P (   < 0.70 )

= 1 - P ( -    / ) < ( 0.70 - 0.60 / 0.05 )

= 1 - P( z < 0.1 / 0.05 )

= 1 - P ( z < 2 )

Using z table

= 1 - 0.9772

= 0.0228

Probability = 0.0228