Question

A teacher believes that 85% of students in the class will want to go on a eld trip to the

local zoo. She performs a hypothesis test to determine if the percentage is the same or di erent from

85%. The teacher samples 50 students and 39 reply that they would want to go to the zoo. For the

hypothesis test, use = 1%.

Answer 1

H0: p = 0.85

Ha: p 0.85

Sample proportion = 39 / 50 = 0.78

Test statistics

z = ( - p) / sqrt [ p ( 1 - p) / n ]

= ( 0.78 - 0.85) / sqrt [ 0.85 ( 1 - 0.85) / 50 ]

= -1.39

For two tailed test.

p-value = 2 * P(Z < z)

= 2 * P(Z < -1.39)

= 2 * 0.0823

= 0.1646

Since p-value > 0.01, Fail to reject H0.

We do not have sufficient evidence to support the claim that proportion is different from 85%