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The mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 1300 voters in the town and found that 45% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%. Testing at the 0.02 level, is there enough evidence to support the strategist's claim?

Sagot :

Answer:

We reject H₀ , we found enough evidence to support the claim

Step-by-step explanation:

Sample size   n = 1300

Sample  proportion  p  = 45 %     p  = 0,45   and   q  = 0,55

Proportion of population     p₀   =  42 %    p₀  = 0,42

Hypothesis Test                

Null Hypothesis                            H₀          p  =  0,42

Alternative Hypothesis                Hₐ          P   >  0,42      

A one-tail test to the right is needed to evaluate the claim

Sample size big enough to consider binomial distribution can approximate to normal distribution

1300*p > 10   1300*q > 10

Significance level   α  = 0,02    

z(c) fom  z-table is   z(c) =  2,05

To compute

z(s)  =  ( p  -  p₀ )  /√ (p*q)/n

z(s)  = ( 0,45 - 0,42 ) /√ (0,45*0,55)1300

z(s)  =  0,03 / 0,014

z(s)  =  2,14

Comparing   z(c)  and  z(s)     z(s) > z(c) then  z(s) s in the rejection region we must reject H₀  we found enough evidence to spport the claim

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