Question

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest of that is smaller In some situations, this choice of d.l. may increase the P-value by a small amount and therefore produce a slightly more "conservative answer A survey of houses and traditional hogans was made in a number of different regions of the modern Navajo Indian Reservation. The following table is the result of a random sample of eight regions on the Navajo Reservation. Area on Navajo Reservation Number of Inhabited Houses Number of Inhabited Hogans Bitter Springs 14 13 Rainbow Lodge 16 14 Kayenta 68 46 Red Mesa 9 Black Mesa 11 15 Canyon de Chelly 28 47 Cedar Point 50 17 Burnt Water 50 18 Does this information indicate that the population mean number of inhabited houses is greater than that of hogans on the Navajo Reservation? Use a 5% level of significance. (Let dhouses - hogans.) (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-talled, or two-tailed test? Ho: Md > 0; M: Md = 0; right-tailed Hot Hd - 0; : Ha < 0; left-tailed Mo: H = 0; M: Hy > 0; right-tailed Ho: Md = 0; Hi Ho 0; two-tailed

Answer 1

let, the given data f calculations! d = 1x1-x2) 1 No. of Inhabited No. of Inhabited houses (x1) Mogans (X2) 14 13 14 68 46 9 32 15 2 22 23 4 47 19 28 so 33 so 18 sd = 136

a) The level of significance, x=0.05 The testing the null & alternative hypothesis, Ho: ideo Vs Hiield>0; right failed b) The student's t. we assume that d ho an approximately normal dista The rest statistic is t=ſna sa Ediz 136, n=8 {d² = 3508 I - Ed - 17 =J=17 L {Ed? - (sd)? n-1 {3508 (136) 7 S = 170,8571 sana n. 8 Isa = 13,0712

The test statistic ta J8x17 85.2254 B.0712 13.0712 t= 6.520 p-values PCZ 76.520) = 0.000164 at x=0.05 f df = 7. P-value = 0.000164 p-value < 0.005