Question 2
Background
The manager of the home loans department of a suburban bank has been asked by an analyst
at the head office of the bank to look at whether the so called problem customers of that bank
have been experiencing more or less mortgage stress in the last year. The branch manager
decides to look at a random sample of n = 100 problem customers. These are customers
whose mortgage repayments are more than four weeks overdue. She finds the number of
weeks overdue for each of these 100 customers and stores these values in cells A2:A101 in
the Excel file Assignment 2 Data.
She refers to the number of weeks overdue a problem customer is with their loan as the X
variable.
In her report she is required to comment on the average level, the variance and the distribution
of the values of the X variable.
Currently the analyst at head office thinks that for the bank customers the average time
overdue that problem loans should be is = 15.5 weeks and the variance of these values
2
should be = 8.
For all of the following questions use a level of significance of = 0.10
Answer the following questions
(a) As part of her preliminary analysis she obtains the descriptive statistics and the histogram
for the X variable. For the histogram she uses the following 15 class intervals
5 < ? 6.5, 6.5 < ? 8, 8 < ? 9.5, 9.5 < ? 11, 11 < ? 12.5, 12.5 < ? 14, 14 < ? 15.5,
15.5 < ? 17, 17 < ? 18.5, 18.5 < ? 20, 20 < ? 21.5, 21.5 < ? 23, 23 < ? 24.5, 24.5 < ? 26.
Using these results discuss the type of distribution that the X variable has. . (5 marks) (b) Obtain the 90% confidence interval for the mean of the X variable and interpret the result.
Briefly discuss how this interval estimate could be used to test the null hypothesis that the
mean is equal to the value of 15.5 that the analyst at head office thinks it is.
What is the size of the error bound for this interval estimate. If she wants an error bound of
B = 0.5 what size sample should she use.
(6 marks)
(c) Using the standard 6 step procedure test whether the average X value is less than the
average of 15.5 that the analyst at head office thinks it is.
(5 marks)
(d) Find the p-value we would use when testing these hypotheses in part (c). Briefly describe
how we interpret and use this value.
(5 marks)
ScholarMatic: Explanation & Answer
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