Question

Chicken Delight claims that 92% of its orders are delivered within 10 minutes of the time the order is placed. A sample of 85 orders revealed that 74 were delivered within the promised time. At the 0.05 significance level, can we conclude that less than 92% of the orders are delivered in less than 10 minutes?

Answer 1

Kindly check explanation

Explanation:

H0 : π ≥ 0.92

H1 : π < 0.92

At α = 0.05

Left tail

Z0.05/2 = Z0.025 = - 1.645

The test statistic

Zstatistic :

(m - p) / σ

Sample size, n = 85

m = 74/85 = 0.87

p = 0.92

σ = sqrt(p(1 - p) /n)

σ = sqrt(0.92(1 - 0.92) / 85)

σ = sqrt(0.0008658)

σ = 0.0294258

σ = 0.0294

Zstatistic :

(m - p) / σ

(0.87 - 0.92) / 0.0294

Zstatistic = −1.700680

Zstatistic = - 1.70

Decision region :

Reject H0: if ;

Zstatistic < Zcritical

-1.70 < - 1.645

Since,

Zstatistic < Zcritical ; then Reject H0.