Math Problem Solver

The laboratory owner aims to minimize sick leave by focusing on disease prevention among employees. Many employees have suffered from pneumonia, leading to productivity issues due to sick leave. A vaccine for pneumococcal pneumonia is available, and the owner believes it's crucial to vaccinate as many employees as possible. Due to limited vaccine availability—enough for only half the employees—two groups emerged: vaccinated and unvaccinated employees. Nurses were dispatched to employees with pneumonia, offering home care and taking sputum samples for identifying the specific pneumonia type. The company tracked the number of pneumonia cases and the specific pneumonia type for each affected employee, accumulating data for statistical analysis. The company wanted to know if providing the vaccine made a difference. Use a Chi-square test to help the company answer this question at the 5% level of significance. Results of the vaccination program Health Outcome Unvaccinated Vaccinated Sick with pneumococcal pneumonia 22 6 Sick with non-pneumococcal pneumonia 7 11 No pneumonia 56 82 NB: The values given in the table above are called the "Observed frequencies", denoted by "O"; the values Expected frequencies are denoted by "E". The calculated Chi-square statistic is given by the formula χ2calc=∑(O−E)2E . (i) The null hypothesis being tested is that there is [Reply with 1 for "there is association" or 2 for "there is no association" between the variables.] Answer for part 1 (ii) Obtain the row totals: Row 1, Row 2 and Row 2, respectively. Answer field 1 for part 2 Answer field 2 for part 2 Answer field 3 for part 2 (iii) Obtain column totals: Column 1 , Column 2, respectively. Answer field 1 for part 3 Answer field 2 for part 3 (iv) Calculate the expected frequencies corresponding to Row 1 of the table. Fill row values from left to right. (roundoff to 4 dp) Answer field 1 for part 4 Answer field 2 for part 4 (v) Calculate the expected frequencies corresponding to Row 2 of the table. Fill row values from left to right. (roundoff to 4 dp) Answer field 1 for part 5 Answer field 2 for part 5 (vi) Calculate the expected frequencies corresponding to Row 3 of the table. Fill row values from left to right. (roundoff to 4 dp) Answer field 1 for part 6 Answer field 2 for part 6 (vii) Obtain (O−E)2 for values in Row1, Row 2 and Row 3, respectively. Fill row values from left to right. (roundoff to 4 dp)Answer field 1 for part 7 Answer field 2 for part 7 Answer field 3 for part 7 Answer field 4 for part 7 Answer field 5 for part 7 Answer field 6 for part 7 (viii) Obtain (O−E)2E for values in Row1, Row 2 and Row 3, respectively. Fill row values from left to right. (roundoff to 4 dp)Answer field 1 for part 8 Answer field 2 for part 8 Answer field 3 for part 8 Answer field 4 for part 8 Answer field 5 for part 8 Answer field 6 for part 8 (ix) Obtain the calculated Ch-square test statistic, χ2calc . Formula is given at the beginning of this question. Answer for part 9 (x) Calculate the degrees of freedom (df) for this Chi-square test Answer for part 10 (xi) Use Chi-square tables to obtain the χ2critical at the degrees of freedom calculated above at α=5% level of significance.Answer for part 11 (xii) Do we reject the null hypothesis or not? [reply with 1 for "Yes" and 2 for "No"] Answer for part 12 (xiii) What is the conclusion? Type 1 for "There is no difference in occurrence of pneumococcal pneumonia between the vaccinated and unvaccinated groups." Type 2 for "There is a significant difference in occurrence of pneumococcal pneumonia between the vaccinated and unvaccinated groups." Answer for part 13 (xiv) Those are the steps you should follow when conduction a non-parametric test of hypothesis using a Chi-square statistic. Reply with 1 to get a bonus mark for making it to this far.😊