Question

**Assigned: In some states the law requires drivers to turn on their headlights when driving in the rain. A highway patrol officer disagrees with this statement and believes that less than (.30) of all drivers follow this rule. As a test, she randomly samples 275 cars driving in the rain and counts the number whose headlights are turned on. She finds this number of cars with headlights on to be 29. Does the officer have enough evidence at 5% level of significance to support her belief that fewer than .30 of all cars follow the rules? One tailed test to the left.

Required in Conclusion section of six step process: Critical ratio/Critical value of Z, Confidence interval and p-value. Use examples in this handout to correctly format the test.

In Assumption section: Include computations to satisfy normal approximation of binomial distribution by solving np≥10 and n(1-p) ≥10. You will have to compute assumption by hand and type the results of each equation onto your homework. (5 points)

Problem You Are Working and Type of Test Z test

Problem Definition: Provide brief description of research objective

Hypothesis

Decision Rule

Test

Conclusion

Interpretation

Assumptions

Answer 1

Ho :   p =    0.3
H1 :   p <   0.3
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Level of Significance,   α =    0.05
critical z value =        -1.645

Decision rule: reject Ho, if z < -1.645

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Number of Items of Interest,   x =   29                  
Sample Size,   n =    275                  
                          
Sample Proportion ,    p̂ = x/n =    0.1055                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0276                  
Z Test Statistic = ( p̂-p)/SE = (   0.1055   -   0.3   ) /   0.0276   =   -7.0401
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Conclusion : reject Ho

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interpretation : There is enough evidence to conlcude that fewer than .30 of all cars follow the rules

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np=29≥10 and

n(1-p)=246 ≥10