A humane society claims that less than 37% of U.S. households own a dog. In a ra
ID: 3313453 • Letter: A
Question
A humane society claims that less than 37% of U.S. households own a dog. In a random sample of
390 U.S. households,153 say they own a dog. At =0.03, is there enough evidence to support the society's claim?
(a) Write the claim mathematically and identify
H0
and
(b) Find the critical value(s) and identify the rejection region(s). (c) Find the standardized test statistic. (d) Decide whether to reject or fail to reject the nullhypothesis, and (e) interpret the decision in the context of the original claim.
A humane soety dan s that-ss thr-37% f U S household, tan deg * random sampl. cf 3" u s userelds, t 53 say thwy o r da At a .0 03, " tere enough "v de ce bo s pport the so-tr's clm a) Whte the dam mshemstically and identity H and Hb) Find the cntical valuels) and icentfy the rejection region(a) (c) Find the standardized test statiztia. (a) Decide whether to re ect or fal to reject the nuil hypothesis and (e) nterpret the ceoson in the conbext of the onginal clam a) Which of tollowing comctyH and H. H p 0.37 C. Ho:ps 0.37 Hapc 0.37 H, P0.37 b) what (are) the cntooi value )? (use comme to separ answer 35 needed. Round to two decam 5 p00 35 needed.) Which of the telowing graphs has the rejacson egion) shaded coectly? a) Whst is the standardized test statistio? z-(Round to to decime pace needed) (d) which of the fallowing eemed tendusin for the test? Fai to reject Interpret your resuts. Choose the comect ser below B. O D. There iseough eidense to iupportté danh that 37% of US households oen à dg. There, erough evidence to support te d8m th81 le55 than 37% of US households own C. There i, not erougn evdence to 5uppon te erm ther le55 than 37% of US households own dog dogExplanation / Answer
(Q1)(1) Ho: p=0.37 (i.e. null hypothesis)
Ha: p<0.37 (i.e. alternative hypothesis)
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(2) It is a one-tailed test.
Given a=0.03, the critical value is Z(0.03)=-1.8808 (from standard normal table)
So rejection region is if Z<-1.8808, we reject the null hypothesis)
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(3)the standardized test statistic is
Z=(phat-p)/sqrt(p*(1-p)/n)
=(153/390-0.37)/sqrt(0.37*(1-0.37)/390)
=0.0223/0.0244
=0.9139
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(4) Since Z=0.9139 is larger than -1.8808, we fail reject the null hypothesis
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(5) So we can not conclude that less than 37% of U.S. households own a dog
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