State DMV records indicate that of all vehicles undergoing emissions testing dur

Question

State DMV records indicate that of all vehicles undergoing emissions testing during the previous year, 73 % passed on the first try. A random sample of 235 cars tested in a particular county during the current year yields 186 that passed the initial test. Does this suggest that the true proportion for this county during the current year differs from the previous statewide proportions?

State DMV records indicate that of all vehicles undergoing emissions testing during the previous year, 73 % passed on the first try. A random sample of 235 cars tested in a particular county during the current year yields 186 that passed the initial test. Does this suggest that the true proportion for this county during the current year differs from the previous statewide proportions? What are the appropriate hypotheses? Ho: = 0.73, HAi 0.73 Ho : = 0.791, HA: 0.73 H0: p=0.73, HA: p + 0.73 Ho: p = 0.791, HA: p 0.791 Submit Answer Tries 0/1 What is the standard error needed for the hypothesis test? (Round the number to 3 digits.) Submit Answer Tries 0/3 What is the value of the test statistic? (Round the number to 3 digits.) Submit Answer Tries 0/3 What is the pvalue? (Round the number to 3 digits.) Submit Answer Tries 0/3

Explanation / Answer

Set Up Hypothesis
Null, H0:P=0.73
Alternate, H1: P!=0.73
Test Statistic
No. Of Success chances Observed (x)=186
Number of objects in a sample provided(n)=235
No. Of Success Rate ( P )= x/n = 0.7915
Success Probability ( Po )=0.73
Failure Probability ( Qo) = 0.27
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.79149-0.73/(Sqrt(0.1971)/235)
Zo =2.1232
| Zo | =2.1232
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 2.1232 ) = 0.03374
Hence Value of P0.05 > 0.0337,Here we Reject Ho

[ANS]
a. H0:P=0.73 ,H1: P!=0.73
b. Standard Error = Sqrt ( (0.7915*0.2085) /235) )
= 0.0265
c. Zo =2.1232
d. P-Value : 0.03374

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