Question

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 Ryerson 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.

a) 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 Minitab for your calculations.

b)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 Minitab for your calculations.

c) Does the confidence interval from part b) confirm your conclusion from part a)? Explain.

Company ID	Number of employees in 2014	Number of employees in 2018
1	33	35
2	21	30
3	19	14
4	23	30
5	54	44
6	11	16
7	8	20
8	5	10
9	22	26
10	11	19
11	8	10
12	6	9
13	5	0
14	7	6
15	13	15
16	5	10
17	12	11
18	17	19

Answer 1

(a) The Paired/Related samples t-test will be used because the sample is related.

The paired sample t-test has four main assumptions:

• The dependent variable must be continuous (interval/ratio).

• The observations are independent of one another.

• The dependent variable should be approximately normally distributed.

• The dependent variable should not contain any outliers.

The graphs are:

The conditions are not met because the data is skewed.

The hypothesis being tested is:

H₀: µ_d = 0

H_a: µ_d > 0

18.000	mean Number of employees in 2018
15.556	mean Number of employees in 2014
2.444	mean difference (Number of employees in 2018 - Number of employees in 2014)
5.415	std. dev.
1.276	std. error
18	n
17	df
1.915	t
.0362	p-value (one-tailed, upper)

Since the p-value (0.0362) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is an increase in the size of the IT firms operating in Ottawa that received support from the CSBFP in 2015.

(b)

18.000	mean Number of employees in 2018
15.556	mean Number of employees in 2014
2.444	mean difference (Number of employees in 2018 - Number of employees in 2014)
5.415	std. dev.
1.276	std. error
18	n
17	df
-0.248	confidence interval 95.% lower
5.137	confidence interval 95.% upper
2.693	margin of error

The 95% confidence interval is between -0.248 and 5.137.

Yes, there is an increase in the size of the IT firms operating in Ottawa that received support from the CSBFP in 2015.

(c) Yes, since the conclusion is the same.