QUESTION 3(10] Chihiro noticed as she looked over company records that productiv

Question

QUESTION 3(10] Chihiro noticed as she looked over company records that productivity seemed to varny according to season. She collected random samples of daily productivity by season and placed them a Low, Medium, or High productivity category. For example the table belorw indicates that ost of 65 randomly selected springtime days 15 days fell into the low productivity category Suppose Chihino asked you to test to see whether average productivity and season are dependent Spring7 Summer Autumn Winter Total Low Medium High Total 15 12 18 35 65 l2. 31 89 e13 42 124 70 129 323 Ho: The avarage predutnity and seacon are mdapendurs Ha: The awokden ean (1 )?State Hypotheses e producftrty and sean are t (2) Test Statistic and Decision Test statistit degree?treedabban C-)(-) 7.12 e13 (3) [2jConclusions (Is there evidence that average productivity is dependent on season?)

Explanation / Answer

the chi-square=sum((Oi-Ei)2/Ei) =20.82 with (r-1)(c-1)=(4-1)(3-1)=6 df

the typical critical chi-square(0.05,6)=12.59, is less than calcuated chi-square=20.82, so we reject the null hypothesis at alpha=0.05 level of significance and conclude that average productivity and seasons are not independent.

Low Medium High Total Spring 15 15 35 65 summer 12 27 40 79 Autumn 18 40 31 89 winter 25 42 23 90 Total 70 124 129 323 observed (O) Expected Expected( E) (O-E) (O-E)2/E 15 65*70/323 14.1 0.9 0.06 12 79*70/323 17.1 -5.1 1.53 18 89*70/323 19.3 -1.3 0.09 25 90*70/323 19.5 5.5 1.55 15 65*124/323 25.0 -10.0 3.97 27 79*124/323 30.3 -3.3 0.37 40 89*124/323 34.2 5.8 1.00 42 90*124/323 34.6 7.4 1.61 35 65*129/323 26.0 9.0 3.15 40 79*129/323 31.6 8.4 2.26 31 89*129/323 35.5 -4.5 0.58 23 90*129/323 35.9 -12.9 4.66 sum= 323 0 323 0 20.82

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.