The general social survey asked 65 randomly selected Republicans, \"How confiden

Question

The general social survey asked 65 randomly selected Republicans, "How confident are you in the federal government?" 60% said they were at least somewhat confident. Is this significantly different from the propportion of all AMerican (0.70) who said they were confident in the federal government? Test the hypothesis HO: p=0.70 vs. HA: p does not = 0.70.

Are the assumptions met for conducting the hypothesis?

A) Yes, because n > 30 and the Republicans are randomly selected

B) No, because the sample proportion is too small

C) No, because the proportion is probably not normally distributed

D) No, because n(1-po) < 10

E) Yes, since npo > 10, n(1-po) > 10, and the Republicans are randomly selected

Explanation / Answer

E) Yes, since npo > 10, n(1-po) > 10, and the Republicans are randomly selected

here Hypothesis:  HO: p=0.70 vs. HA: p does not = 0.70

for n=65 therefore std error =(p(1-p)/n)1/2 =0.0568

smple proportion phat=0.60

therefore test statistic z=(phat-p)/std error =(0.6-0.70)/0.0568=-1.7593

for above test statistic p value =0.0785

please revert on level of significance for making a deciison

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