Question 2 The Reserve Bank of Australia (RBA) slashed the official cash rate to a record low of 0.1 per cent in 2020 as an emergency response to the COVID-19 pandemic, An economist is Not yet saved interested in the average principal and interest repayment for a standard variable rate home loan entered into under the record low official rate. In mid-2020, 35 home loan customers Marked out of with loans of the same characteristics were randomly sampled and asked how much they paid per month for their home loans. The descriptive statistics are shown in the table below. 14.00 Flag Descriptive Statistics for Home Loan Repayments in mid-2020 question Mean Standard Error Standard Deviation Count 1482.44 24.05 142.28 35 Hint: For the first three questions you need to use the sample statistics (mean and standard deviation) to calculate a standardised value from a z or t distribution to be able to calculate this probability. We can assume that the average monthly repayment is normally distributed. 1. (1 mark) What is the probability that a randomly selected home loan customer, that the monthly repayment is less than $1437.09? (3dp) 2. (1 mark) What is the probability that a randomly selected home loan customer, that the monthly repayment is greater than $1511.92? (3dp) 3. (1 mark) What is the probability that a randomly selected home loan customer, that the monthly repayment is between there are between $1437.09 and $1511.92 ? (3dp) The RBA raised official interest rates for the first time in 11 years to curb surging inflation. All of Australia's biggest banks have lifted their mortgage rates, matching the Reserve Bank's 25-basis point increase. To examine the impact on the home loan customers paying interest and principal, the same group of customers were contacted and asked about their current monthly repayment and the summary statistics for their answers are recorded in the table below. Descriptive Statistics for Home Loan Repayments in mid-2022 Mean Standard Error Standard Deviation Count Current monthly repayment 1788.03 14.18 83.91 35 Differences in monthly repayment 305.59 25.49 150.80 35 Answer the following questions, if needed, by using Excel to analyse the data.\fT. {3 marks} Calculate a 95% condence intewal to estimate the average change In monthly repayment paid by all home loan customers between mid2020 and mid2022. Answer the following questions, if needed, by using Excel to analyse the data. Research Question: An economist is interested in assessing whether the average monthly repayment has changed since 2020 4. (1 mark) The most appropriate hypothesis test for these data is 5. (2 marks) What is the absolute value of the test statistic ? a paired t-test for comparing means 6. (2 marks) Is the p-value for this test statistic greater or less than a one-sample t-test for a population mean 7. (3 marks) Calculate a 95% confidence interval to estimate the a a one-sample z-test for a population mean ome loan custor The Absolute Value of the Critical Value for a 95% confidence interval a two-sample t-test for comparing means6. [2 marl-cs) Is the pvalue for this test statistic greater or less than 0.05? 'r'. (3 marl-cs) Calculate a 95% condence interval to estimate the average ll home loan customers between mid2020 and mid2022. __ _ _ the pvalue is greater than 0.05 The Absolute Value of the Critical Value for a 95% condence Interval Is the pvalue is less than 0.05 Lower Bound = S [2dp] Upper Bound = S [2dp] For the same condence interval (95%). decreasing the sample size n will For the same confidence interval (95%), decreasing the sample size n will 8. (1 mark) the value of the standard error (SE= ) of the estimates 9. (1 mark) the width of the confidence interval 10. (1 mark) makes our estimated interval accurate Copyright @ Macquarie University. Copying it or all of the contents in any form is prohibited. A. more B. less C. no change