Question 1 - Canada Small Business Financing Program (3 parts, 15 marks) One of the support programs of the Government of Canada for small businesses is Canada Small Business Financing Program (CSBFP). Under the CSBFP, the Government of Canada shares the risk of default with the lender by guaranteeing 85 percent of the lender's net eligible losses. Under this program, small businesses may obtain financing for the following assets: real property (immovables), equipment, and leasehold improvements. A fourth-year finance student at Telfer is interested in seeing whether this program contributes to the growth of small businesses. She randomly selected 18 IT firms operating in Ottawa that received support from the CSBFP in 2015. She interviewed these companies and recorded the number of employees in 2014 and 2018. These numbers are provided in dataset CSBFP.

a) [8 Marks] Carry out a hypothesis test to determine whether there was any increase in the size of the IT firms operating in Ottawa that received support from the CSBFP in 2015. Explain your approach in choosing a test, state the corresponding conditions, and show by using an appropriate graph if the conditions are met. Copy the graph and use a 5% significance level. You may use MS Excel or other software for your calculations.-Are the samples independent? The same entity (i.e. company) is contributing to each record (one for 2014 and another for 2018). If not, we should do paired t test -Check assumptions: Randomization, independence, 10% condition, normality of difference.

For checking normality of difference (i.e. ?i = 2014 ? 2018), draw a boxplot of the ?i value and comment whether they look like normal distribution -Steps: (a) Hypotheses (should be using the subscript 'd'): Look for the directional phrase 'growth'. If growth is expected and difference is calculated like ?i = 2014 ? 2018, then ?d should be negative. On the other hand, if growth is expected and difference is calculated like ?i = 2018 ? 2014, then ?d should be positive. So, your hypothesis depends how you calculate the difference value ?i. Please note that EXCEL is doing the difference like ?i = 2014 ? 2018, so if you use EXCEL builtin menu, your alternative hypothesis should be ?d

b) [6 Marks] Using a confidence level of 95%, was there an increase in the size of the IT firms operating in Ottawa that received support from the CSBFP in 2015? Calculate the corresponding confidence interval manually and state your conclusion. You may use MS Excel or other software for your computations.

A B C D E 1 Company Number f employees in 201 Number of employees in 2018 1 33 35 N 2 21 30 19 14 4 23 30 5 54 44 6 6 11 16 8 7 8 20 9 8 5 10 10 9 22 26 11 10 11 19 12 11 10 13 12 9 14 13 0 15 14 6 16 15 13 15 17 16 10 18 17 12 11 19 18 17 19 20 21 22 23