Question

Bob the Quality Control Engineer wishes to determine the mean mass of apples grown in Tallula's orchard. A sample of 7 randomly-chosen apples has a mean mass of 112 g with a sample standard deviation of 32 g. Using a t-distribution, find a 90% one-sided lower confidence bound on the population mean mass of apples in grams. Give your answer to one decimal place.

Answer 1

on Soln Here, we have to find the 90% one sided lower confidence bound on the population mean mass of apple in grams on the basią of random sample of size 7 with mean 112 g and standard deviation of 32 329. Now, one sided confidence interval 18 P( Ti su ) = 90% we have to find to Now consider PC -00 < t < c) = 0.90 for any c at (7-1) d.f ie 6 d. f. comparing from t distribution table, we get the value of c ig 1.440. PL-00sts 1.449 = 0.90 X-4 since sia and here 112, S = 32, n = 7.59 < 1.44) 32/6 PL-005 112-M€ 12.0949x1.44) = 0.90 PL-005112 -M< 17.4167) = 0.90 PL-005-4 <-94.5833) =0,90 PC 94.5833 5 4 500) = 0,90 so lower confidence bound 1B 94.6. ie ta = = 0.90 PL-00€ 112-4