A sample of 293 urban adult residents of a particular state revealed 64 who favo

Question

A sample of 293 urban adult residents of a particular state revealed 64 who favored increasing the highway speed limit from 55 to 65 mph, whereas a sample of 190 rural residents yielded 72 who favored the increase. Does this data indicate that the sentiment for increasing the speed limit is different for the two groups of residents? Test H_0: P_1 - P_2 = 0 versus H_a: P_1 - P_2 # 0 using alpha = 0.05, where p_1 refers to the urban population. (Round your test statistic to two decimal places and your P-value to four decimal places.) z =P-value =-3.770 p- value = 0002 State the conclusion in the problem context. Reject H_0. The data does not suggest that the sentiment for increasing the speed limit is different for the two groups of residents. Reject H_0. The data suggests that the sentiment for increasing the speed limit is different for the two groups of residents. Fail to reject H_0. The data suggests that the sentiment for increasing the speed limit is different for the two groups of residents. Fail to reject H_0. The data does not suggest that the sentiment for increasing the speed limit is different for the two groups of residents. If the true proportions favoring the increase are actually p_1 = 0.22 (urban) and P_2 = 0.39 (rural), what is the probability that H_0 will be rejected using a level 0.05 test with m = 293, n = 190? (Round your answer to four decimal places.) 0.0001

Explanation / Answer

Null, no Significance between them Ho: p1 = p2
Alternate, There Is Significance between them H1: p1 != p2
Test Statistic
Sample 1 : X1 =64, n1 =293, P1= X1/n1=0.218
Sample 2 : X2 =72, n2 =190, P2= X2/n2=0.379
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.282
Q^ Value For Proportion= 1-P^=0.718
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.218-0.379)/Sqrt((0.282*0.718(1/293+1/190))
Zo =-3.832
| Zo | =3.832
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =3.832 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != -3.8315 ) = 0.0001
Hence Value of P0.05 > 0.0001,Here we Reject Ho

[ANSWERS]
Z = -3.832
P = 0.0001
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != -4.0351 ) = 0.0001

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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