In a recent survey 1500 U.S adults 795 said that they were in favor of more stri

Question

In a recent survey 1500 U.S adults 795 said that they were in favor of more stringent background checks for purchase of guns. At the 5% significance level test the hypothesis that a majority of U.S. adults favor more stringent background checks. a. Verify that the sample size is large enough. b. Define the parameter and state the null and alternative hypotheses c. Determine the standard error. d Determine the test statistic e. Find the p-value f. Determine the result of the test. g. State the conclusion in the context of the problem.

Explanation / Answer

a) here p=0.5 ;' hence np=1500*0.5>10 and n(1-p)=1500(1-0.5)>10

hence requirement is fulfilled.

b)parameter is proportion favoured moe stringent rules =0.5

null hypothesis: p=0.5

alternate hypothesis: p>0.5

c)std error=(p(1-p)/n)1/2 =0.0129

d)phat =795/1500=0.53

test stat z=(phat-p)/std error =(0.53-0.5)/0.0129 =2.3238

e) p value for above one tailed test =0.0101

f)as p value is less then 0.05 level ; we reject null hypothesis

g)we conclude that majority of US adults favoured more stringent background checks

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