In one Eastern European country, it takes an average of 2 weeks for an average patient to recover from pneumonia after taking antibiotics A

5. (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 recovery time 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 recovery time of those taking antibiotic B is 1.5 weeks with the standard 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 significance level of 5%. (b) A shipping company needs to choose among three different routes, Routes 1, 2, and 3, to go from point C to point D. Members of the analytics team randomly select 18 truck drivers and randomly assign 6 of them to each route. Then the hours from point C to point D are measured. The sample mean time for Routes 1, 2, 3, are 5.8650, 6.0367, 5.6333, respectively; and the sample standard deviations are 0.2512, 0.4905, and 0.3565, respectively. Is there a difference in the mean trip time among the routes at 5% significance? 6. In a back office of a real estate agent company, an analyst seeks to develop a model to predict the assessed value (in thousands of dollars) by using the size of the houses (in thousands of square feet) and the age of the houses (in years). To do this, she took a random sample of 15 houses to perform a regression analysis as follows: SUMMARY OUTPUT Regression Statistics Multiple R 0.909120107 R Square 0.826499369 Adjusted R Square 0.797582598 Standard Error 2.168165527 Observations 15 ANOVA df SS MS F Significance F Regression a 268.724699 2.72776E-05 Residual b 56.41130101 4.700942 Total 14 325.136 Coefficients Standard Error t Stat P-value Intercept 163.7751236 5.407173152 30.28849 1.05E-12 Size 10.72518298 3.014327189 Age -0.28425435 0.083598359 -3.40024 g (a) State the multiple regression equation. Interpret the meanings of the coefficients for size and age. (b) Test the validity of this multiple regression equation at the significance level of 1%. Show your reasoning. (c) Is there a linear relationship between the assessed value of the house and its size? Test this claim at the significance level of 1%. (d) The analyst claims that there is a negative relationship between the assessed value of the house and its age. Test her claim at the significance level of 1%