1. Micro, Small and Medium Enterprises (MSMEs) are known to contribute significantly to a country's economy. The infographic below highlights some of these contributions to the Jamaican economy. MINISTRY OF INDUSTRY, COMMERCE, AGRICULTURE & FISHERIES POLICY MSME DIVISION PROJECTS PARTNERSHIP MSME FACTS They represent over 90% of the private sector MSMEs represent 34% of the employed labour force Contributed over $100 billion in taxes Source: Ministry of Industry, Commerce, Agriculture and Fisheries, Government of Jamaica While making significant contributions, many MSMEs fail because of their limited knowledge of financial management and processes. In an effort to assist this group of businesses, many financial institutions have instituted departments that solely assist MSMEs. This includes notifying these businesses of special financial products and hosting educational seminars. One bank would like to determine if their education programme is effective. To do so, they collect data from a sample of MSMEs that participated in an educational seminar series. The organisers of the seminar gave the participants, who were CEOs of MSMEs, a knowledge test before and after the seminar. The results are presented below. Paired Samples Statistics Std. Error Mean N Std. Deviation Mean Pair 1 Post 6.8097 122 .82471 .07467 Pre 7.3776 122 1.06864 .09675 Paired Samples Correlations N Correlation Pair 1 Post & Pre 122 .551 Sig. .000 Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Upper t df Sig. (2-tailed) -.40246 -6.797 121 .000 Pair 1 Post-Pre Mean -.56787 Std. Deviation Std. Error Mean Lower .92285 .08355 -.73328 2.00 1.00 .00 -1.00 -2.00 -3.00 Expected Normal Value Normal Q-Q Plot 0 1 2 Observed Value a) Using the data provided, estimate the difference between pre-test and post-test scores at the 90% level of confidence. b) What is the margin of error for your result in (a)? c) Use your result from (a) to determine if there is a difference in the pre-test and post-test scores. i) Using the information provided, do you have any reason to be concerned about the validity of your results? Give reasons for your answer.