Question

Professor Smith loves dark chocolate, and she would like to find out the proportion of the population that shares her preference. She randomly sampled 750 people, and 130 people chose dark chocolate. To construct a 95% confidence interval, she should use:

Answer 1

For the test,

Let, binomial population parameter = p0

successes i.e. people chose dark chocolate = r = 130

observations i.e. no. of people choosen randomly = n = 750

observed proportion, = r / n = 0.17333.

We have to test,

H0: p = p0   vs H1: p p0

Test statistic:

, under H0, Z ~ N(0,1)

For = 0.05, we reject H0 if Z > Z0.025, where Z0.025 is the 1-0.025 percentile of the standard normal distribution.

so the confidence interval is,

= ( 0.14624179 , 0.200424209 )