Question

7.13 A marketing survey is conducted in which students are to taste two different brands of soft drink. Their task is to correctly identify the brand tasted. A random sample of 200 students is taken. Assume that the students have no ability to distinguish be- tween the two brands. a. What is the probability that the sample will have between 50% and 60% of the identifications correct? b. The probability is 90% that the sample percentage is contained within what symmetrical limits of the population percentage? c. What is the probability that the sample percentage of correct identifications is greater than 55%?

Answer 1

Ans:

population proportion=0.5

n=200

standard error of p-hat=sqrt(0.5*(1-0.5)/200)=0.0354

a)

z(0.5)=0

z(0.60)=(0.60-0.50)/0.0354=2.82

P(0<z<2.82)=P(z<2.82)-P(z<0)

=0.9976-0.5=0.4976

b)

lower limit=0.5-1.645*0.0354=0.442

upper limit=0.5+1.645*0.0354=0.558

c)

z=(0.55-0.5)/0.0354

z=1.414

P(z>1.414)=0.0786