Critical Values of t (1-tailed probabilities) Degrees of freedom t.100 t.050 t.025 t.010 t.005 1 3.0777 6.3138 12.7062 31.8207 63.6574 2 1.8856 2.9200 4.3027 6.9646 9.9248 3 1.6377 2.3534 3.1824 4.5407 5.8409 4 1.5332 2.1318 2.7764 3.7469 4.6041 5 1.4759 2.0150 2.5706 3.3649 4.0322 6 1.4398 1.9432 2.4469 3.1427 3.7074 7 1.4149 1.8946 2.3646 2.9980 3.4995 8 1.3968 1.8595 2.3060 2.8965 3.3554 9 1.3830 1.8331 2.2622 2.8214 3.2498 10 1.3722 1.8125 2.2281 2.7638 3.1693 11 1.3634 1.7959 2.2010 2.7181 3.1058 12 1.3562 1.7823 2.1788 2.6810 3.0545 13 1.3502 1.7709 2.1604 2.6503 3.0123 14 1.3450 1.7613 2.1448 2.6245 2.9768 15 1.3406 1.7531 2.1315 2.6025 2.9467 16 1.3368 1.7459 2.1199 2.5835 2.9208 17 1.3334 1.7396 2.1098 2.5669 2.8982Internet company Gurgle is carrying out testing on the efficiency of its search engine. A sample of 55 searches have been carried out and the time taken to display the results has been recorded for each search. The mean search time for the sample was calculated as 0.1224 seconds. The standard deviation of the search times for the sample was calculated as 0.0134 seconds. The population standard deviation of G Ll r [6 search times is unknown. 3) Select all the techniques that are commonly used to construct a confidence interval for the mean when the population standard deviation [0) is unknown: C] Approximate the population standard deviation (0) with the sample standard deviation (5) C] Replace the sample size (n) with n1 E] Decrease the confidence level to compensate for the increased margin of error [:1 Approximate the standard normal distribution with the Student's t distribution b) Calculate the upper and lower bounds of the 90% condence interval for the mean search time for the Gurgle search engine. You may find this Student's t distribution table useful. Give your answers in seconds to 4 decimal places. Upper bound = seconds Lower bound : seconds BU