Question

14. Each person in a random sample of 50 was asked to state his/her sex and preferred colour. The resulting frequencies are shown below Colour Red Blue Green Male Female 14 6 Sex 15 A chi-square test is used to test the null hypothesis that sex and preferred colour are independent. Which of the following statements is a correct decision about the null hypothesis? (a) Reject at the 0.005 level. (b) Reject at the 0.01 level but not at the 0.005 level (c) Reject at the 0.025 level but not at the 0.01 level (d) Reject at the 0.05 level but not at the 0.025 level (e) Accept at the 0.05 level. 15. The following data were obtained from a company which manufactures special plastic containers which are to hold a specified volume of hazardous material. On each of the three 8 hour shifts workers are able to make 500 of the containers. Some containers do not meet specifications as required by the company's customer because they are too small, others because they are too large. Conformance to Specification Shift Too Small Within Spec. Too Large 4pm midnight 12 If conformance to specifications is independent of shift, the expected num- ber of containers that meet specification on the 4pm shift is (a) 166.7 (b) 443 (c) 33 (d) 444.3 e) 500 36 24 452 443 438 12 50

Answer 1

"Page (1) Null hypothesis (H_0): - Sex and preferred color are independent o = observed frequency E = Expected frequency test statistic , x^2 = 8.6 critical value of x^2 (x^2 cost) foe x^2 table: Df = (c - 1) (r -1) = (3 -1)(2 - 1) = 2 At alpha = 0.01, X^cost = 9.210 implies Fail to reject H_0 At alpha = 0.025 x^2 cost = 7.378 implies Reject H_0 At alpha = 0.05 x^2 crt = 5.991 implies Reject H_0 At alpha = 0.005, x^crt = 10.597 implies Fail to reject H_0 Page (2) Df = Degrees of freedom c = No. of columns = 3(Red, Blue, Green) R = No. of rows = 2(male & female) If X^2_(8.6) < x^2_cost , we fail to reject null hypothesis (H_0) Thus, among the given options, option is correct i.e "" Reject at the 0.025 level but not at the 0.01 level"""