Question

Tommy is a commercial crabber. To compare this years catch to last years catch, Tommy measured 35 of the crabs he caught this year. The following are the measurements in inches of the 35 crabs across the widest part of their body from tip of spine to tip of spine: 6.25 7.1 6.8 6.85 6.2 7.3 6.9 6.6 7.25 6.9 6.8 6.75 7.1 6.8 6.25 7.0 6.7 6.75 6.1 6.3 6.9 7.0 6.85 6.75 6.5 6.3 6.45 6.5 7.2 6.9 6.9 7.1 7.0 6.9 6.75 Last year the average size of the crabs that Tommy caught was 6.65 inches. Is there enough evidence to prove that the crabs Tommy caught this year are bigger on average than the crabs caught last year? a. Calculate the p-value. Round your answer to four decimal places. b. Using a level of significance of 0.05, choose the best conclusion. C. If Tommy had used a level of significance of 0.01, would he have reached the same conclusion?

Answer 1

Solution s from Sample, Mean, Eu Ex 6.25+...+6175 n 35 r = 6.7628 Staudeed Deviation, S :- il- Grink c) - 35(6.25-6.7628) +--- +5.75-6-7612 + 1 s=0.3132 . Test hypothesis Ho: M - 6.65 Hai lu 76.65. Test Statistics, 7= -༥ slun ll 6.7628-6.65 0-3132/135 = 2.1306 Z=2.1306 alP-value = 0.0165 using z-table, right tail. Since P-value is less then o.o5. by Reject Ho we have sufficient Evidence to support the claim c7 If we use diool , P-value >0.01 fail to Reject Ho. we have no sufficient Support the clan Evidace to