STAT 1181 Assignment 5 (40 marks) Due April 4, 2024
1. According to research, the average non-mortgage debt of Canadians is $23000. A simple random
sample of 38 Canadians was selected, and their average non-mortgage debt was found to be
$21000. Assume the population standard deviation of non-mortgage debt is $4600. At the 0.01
level of significance, is there sufficient evidence to conclude that the average non-mortgage debt
of Canadians has decreased? (10 marks)
a) Define the parameter of interest in the context of the question. (1 mark)
Ans-: The parameter of interest is mu ,the true mean non-mortgage debt of all Canadians.
b) Set up the null and alternative hypotheses in terms of the parameter. (2 marks)
Sample mean=$21000
Population mean under the null hypothesis=$23000
Population standard deviation=$4600
Sample size=38
Z= (21000-23000)/(4600/ √38)
Z value = -2.68
H0 = mu=$23000 The average non-mortgage debt among Canadians is 23000, indicating no
change.
Ha = mu<$23000 The average non-mortgage debt among Canadians has decreased from 23000.
c) Calculate the test statistic. Find the p-value. Check the required condition(s) to validate the
pvalue. (3 marks)
Ans
Looking at the distribution table lower tail P value is approximately 0.0037.
d) Interpret the p-value in the context of the question. (2 marks)
0.0037 indicates a very low probability of observing a sample mean
These rejects the null hypothesis and conclude that the average non-mortgage debt of Canadians
has decreased from 23000. This suggest strong evidence against the null hypothesis at 0.01 level
of significance.
e) What conclusion can be drawn? (2 marks)
Answer
Since the p-value is less than the significance level of 0.01, we reject the null hypothesis.
Therefore, there is sufficient evidence to conclude that the average non-mortgage debt of
Canadians has decreased from the previously assumed average of $23,000.
2. Apple claims that the average wait time for a customer calling the Apple Care support line is 180
seconds. A simple random sample of 35 customers was selected, and their average wait time was
found to be 190 seconds. Assume the population standard deviation of wait time is 45 seconds.
At the 5% level of significance, is there enough evidence to conclude that the average wait time
for a customer calling the Apple Care support line is more than 180 seconds? (10 marks)
a) Define the parameter of interest in the context of the question. (1 mark)
The parameter of interest is mu, the true mean wait time for all customers calling the Apple Care
support line.
