Question

1. According to research, the average non-mortgage debt of Canadians is $23800. A simple random sample of 60 Canadians was selected, and their average nonmortgage debt was found to be $22500. Assume the population standard deviation of non-mortgage debt is $4600. Is there sufficient evidence to conclude that the average non-mortgage debt of Canadians has decreased?

Use α = 0.05.

a) State the null and alternative hypotheses in the context of the question.

b) Calculate the value of the test statistic. Check the required condition(s) to validate the test statistic.

c) Find the p-value.

d) What conclusion can we draw?

Answer 1

Given :

n = 60

= 22500

T

$\sigma$= 4600

Hypotheses test

H0:μ=23800

Ha:μ<23800

Test statistic

z =
T
- $\mu$ / $\sigma/n$

= -2.1891

= - 2.19

p- value

p value with test statistic z = -2.19 is

p- value =

	=	P(Z<Zobs)
	=	P(Z<−2.19)
	=	P(Z>2.19)
	=	1−P(Z<2.19)
	=	1−0.98574
	=	0.0143

p value = 0.0143

conclusion

the p-value = 0.01426 < α = 0.05 we reject H0 and conclude that at the 5.0 % level of significance there is sufficient evidence to support a claim that  the average non-mortgage debt of Canadians has decreased