Question

A market researcher working for the bank wants to know if the distribution of the number of applications for home loan is uniformly distributed across all the working days of the week. She takes a random sample of 200 applications. The table below shows how many applications were submitted on each day of the week.

Day	Applications
Monday	32
Tuesday	42
Wednesday	49
Thursday	41
Friday	36

a) If the number of applications is uniformly distributed across all days of the week, how many would you expect on each day?
b) To see if these results are unusual, should you perform a goodness-of-fit test or a test of independence?
c) State your hypotheses.
d) How many degrees of freedom are there?
e) Find ?2 and the P-value.
f) State your conclusion (use α = 0.05) in the context of the question.

Answer 1

Chi-Square Goodness-of-Fit Test for Observed Counts in ... applications

Using category names in Day

Observed and Expected Counts

===============================

a) 200/5= 40

===============================

b)  test of independence

===============================

c) H0: The data is uniformly distributed

H1: The data is not uniformly distributed

===============================

d) df = 5-1 = 4

===============================

e)

Category	Observed	Test Proportion	Expected	Contribution to Chi-Square
Monday	32	0.2	40	1.600
Tuesday	42	0.2	40	0.100
Wednesday	49	0.2	40	2.025
Thursday	41	0.2	40	0.025
Friday	36	0.2	40	0.400

Chi-Square Test

N	DF	Chi-Sq	P-Value
200	4	4.15	0.3861

P-value = 0.3861

==============================

f) P-value is greater than 0.05 so, fail to reject H0, and can conclude the data is uniformly distributed