Question

A school district claims that the normal attendance rate for their schools is 95%. An educational advocate believes that the true figure is lower. She chooses a school day in October and chooses 120 random students from the district. On that day, 87.5% of the students attended school. Can she conduct a hypothesis test to determine whether the proportion of students who attend school is lower than 0.95?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.95

H_a : p 0.95

n = 120

= 0.875

P₀ = 0.95

1 - P₀ = 1 - 0.95 = 0.15

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.875 - 0.95 / [0.95 * 0.15 /120 ]

= -3.77

Test statistic z value = - 3.77

P-value = 0.0001