A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample c 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.7; 2.9; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4. NOTE: If you are using a Student's tdistribution, you may assume that the underlying population is normally distributed. (In general, you must rst prove that assumption, though.) El Part (a) (i) Round your answer to two decimal places. i = (rounded to two decimal places) (ii) Round your answer to two decimal places. 3, = (rounded to two decimal places) (iii) Enter an exact number as an integer, fraction, or decimal. (iv) Enter an exact number as an integer, fraction, or decimal. n-1=l Construct a 95% confidence interval for the population mean length of time. (i) State the confidence interval. (Round your answers to two decimal places.) (ii) Sketch the graph. OL C.L. =[ N X (iii) Calculate the error bound. (Round your answer to two decimal places.) + Part (f)