New car dealers in California have stated that 45 of new veh

New car dealers in California have stated that 45% of new vehicle sales are trucks. A research group in California believes that this is no longer true. They randomly select 200 new vehicle sales and find 100 are trucks. Use the .10 level of significance, and determine if the data suggest that the percent of trucks has changed. What are the Null and Alternative hypotheses? What is the rule for rejecting the Null?

Solution

Set Up Hypothesis
Null, H0:P=0.45
Alternate, H1: P!=0.45
Test Statistic
No. Of Success chances Observed (x)=100
Number of objects in a sample provided(n)=200
No. Of Success Rate ( P )= x/n = 0.5
Success Probability ( Po )=0.45
Failure Probability ( Qo) = 0.55
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.5-0.45/(Sqrt(0.2475)/200)
Zo =1.4213
| Zo | =1.4213
Critical Value
The Value of |Z | at LOS 0.1% is 1.645
We got |Zo| =1.421 & | Z | =1.645
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 1.42134 ) = 0.15522
Hence Value of P0.1 < 0.1552,Here We Do not Reject Ho

[ANSWERS]
1. H0:P=0.45 , H1: P!=0.45
2. LOS 0.1% is Reject Ho, if Z<-1.645 OR Z>1.645