Kim Engineering Inc. is a large manufacturing company in British Columbia. A Human Resources consultant from Kim Engineering would like to know whether the average annual number of sick days taken by the employees significantly decreased after the new medical insurance package had been introduced in January 2020. Six people were randomly selected, and the numbers from the Human Resources files you can see in the table below. These numbers show how many sick days each employee took in 2019 and 2020. Based on this table, can we conclude at a 5% significance level that the annual number of sick days decreased, on average (2019 is more than 2020)? Assume that the population of differences d = 2019 sick days - 2020 sick days is approximately normally distributed and use the t-distribution. For parts (a), (b), (c), round your answers to 2 decimal places. (a) d = You MUST answer part (a) before filling in the two right columns in the table. (b) Fill in the table below. 2019 2020 d = Worker Sick Sick d - d Before - After (d - d)2 Days Days 7 5 0 2 10 9 3 11 5 5 2 5 12 4 6 14 7 Total{c} The standard deviation for the differences is sd = At a 5% significance level, test the company's claim. Use the t-test for matched pairs and the formula involving the mean of the differences pg, 5 _ r. = \"d (f) 4?: {d} State the null and alternative hypotheses, and identify which one is the claim. Which one is the claim: , (Note: pd = D} _H1 _HD For parts [e], [f] use the correct sign for the t-value and test statistic' either positive or negative, and round your answers to 3 decimal places. {e} What is the critical t-value [from the Student t-table}? {f} What is the test statistic? {g} Is the null hypothesis rejected