Question

The manager of a fast-food restaurant wants to reduce the proportion of drive-through customers who have to wait longer than 2 minutes to receive their food after placing an order. Based on store records, the proportion of customers who had to wait longer than 2 minutes was p = 0.63. To reduce this proportion, the manager assigns an additional employee to assist with drive-through orders. During the next month, the manager will collect and random sample of drive through times and see if they have decreased.

a. What is the parameter of interest in this problem?

b. State the null and alternative hypotheses

c. Describe a Type I and Type II error in this setting and explain the consequences of each

Answer 1

The manager of a fast-food restaurant wants to reduce the proportion of drive-through customers who have to wait longer than 2 minutes to receive their food after placing an order.

Based on store records, the proportion of customers who had to wait longer than 2 minutes was p = 0.63.

a)  parameter of interest

Here Parameter of interest is the proportion of drive-through customers who have to wait longer than 2 minutes to receive their food after placing an order.

P = 0.63(Given)

b)

The manager of a fast-food restaurant wants to reduce the proportion of drive-through customers who have to wait longer than 2 minutes to receive their food after placing an order.

We want to test that additional employees will reduce the proportion of drive-through customers who have to wait longer than 2 minutes to receive their food after placing an order.

Given that the Proportion is 0.63

.P=0.63

Ho:- P = 0.63

Vs

Ha:- P < 0.63

i.e

Ho: - additional employees do not reduce the proportion of drive-through customers who have to wait longer than 2 minutes to receive their food after placing an order.

Vs

Ha:- additional employees reduces the proportion of drive-through customers who have to wait longer than 2 minutes to receive their food after placing an order.

c) Type I error:- Reject Null hypothesis when it is true

Here we may conclude that the additional employees reduce the proportion of drive-through customers who have to wait longer than 2 minutes to receive their food after placing an order. but actually it not reduce the proportion of customers waiting.

Here we consequence is the manager will think that he reduced waiting time but actually it is not. so the customer will be unsatisfied with the company.

Type II error: Do not reject the null hypothesis when the null hypothesis is false.

Here we may conclude that the additional employees do not reduce the proportion of drive-through customers who have to wait longer than 2 minutes to receive their food after placing an order. but actually it reduces the proportion of customers waiting.

The consequence is the manager will have to find another way to reduce proportion & it may cost him money & manpower but in actual no need of it.