Question

Before shopping on-line became very popular with consumers a few years ago, 10% of retail outlets in Canada closed their doors each year (i.e., went out of business). A random sample of 200 retail outlets across Canada which were open at the beginning of 2019 were randomly selected for a study. At the end of 2019, 25 or these outlets were no longer open. At the .10 level of significance, is there sufficient evidence that the proportion of all Canadian retail outlets that closed in 2019 is greater than the proportion that closed before shopping on-line became very popular? In answering this question, complete the following in the spaces provided (including diagrams):

Please provide hypothesis, test staistic, decision rule, p-value, and conclusion.

Answer 1

We are going to test for the population proportion. Previously 10% of retail outlets in Canada closed their doors each year (i.e., went out of business) Before shopping on-line became very popular. So we want to test the claim that  the proportion of all Canadian retail outlets that closed in 2019 is greater than the proportion that closed before shopping on-line became very popular.

= x /n

Test Stat :

The test is one right tailed test.

p-value = P( Z > |Test stat|)

=1 -  P( Z < |Test stat|) .................using normal distribution tables.

Null hypothesis	p =< 0.1
Alternative hypo	p > 0.1
Null p	0.1
x	25
n	200
Sample p	0.125
SE	0.0234
Test Stat	1.0690
p-value	0.14231		P(Z < 1.07) = 0.8577
Since p-value > 0.1
Decision	Reject null hypothesis
Conclusion	There is insufficient evidence to conclude that the proportion is greater.