need help in this probability and statistic question with steps, thank

(a) In one Eastern European country, it takes an average of 2 weeks for an average patient to recover from pneumonia after taking antibiotics A. Recently, a competitor claims that it has developed another antibiotic, called antibiotic B, that has a shorter average recover lime of pneumonia than that of antibiotic A. To test its claim, it took a random sample of 102 patients in which half took antibiotics A and another half took antibiotics B. The average recovery time of those taking antibiotic A is 2 weeks with the standard deviation 3 days. On the other hand, the average recover time of those taking antibiotic B is 1.5 weeks with the stande deviation 5 days. Assuming that each population of patients taking either antibiotic A or antibiotic B is normally distributed, test the competitor's claim at the signicance level of 5%