Question

The national average for non-mortgage debt is $31,531 in Canada with a standard deviation of $5,215. The average non-mortgage debt in a randomly selected sample of 60 Kingston residents is $29,132. Do Kingstonians have lower non-mortgage debt levels than the rest of the country?

Answer 1

Null Hypothesis H0: = $31,531

Altenative Hypothesis Ha: < $31,531

Sample mean, = $29,132

Population standard deviation = $5,215

Since we know the true population standard deviation we will conduct one sample z test.

Standard error of mean, SE = / = 5215 / = 673.2536

Test statistic, z = ( - ) / SE =  (29132 - 31531) / 673.2536 = -3.56

p-value = p(z < -3.56) =  0.0002

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0.

There is sufficient evidence at 5% significance level to conclude that the true mean non-mortgage debt levels of Kingstonians is lower than the national average of $31,531