Gallop conducted a national survey of 1008 American adults a

Gallop conducted a national survey of 1008 American adults, asking “As you may know, as part of its efforts to investigate terrorism, a federal government agency obtained records from larger U.S. telephone an Internet companies in order to compile telephone call logs and Internet communications. Based on what you have heard or read about the program, would you say that you approve or disapprove of this government program?” Of those surveyed, 534 said they disapprove. At the 10% significance level, do the data provide sufficient evidence to conclude that a majority of American adults disapprove of this government surveillance program?

What are the null and alternative hypothesis?

What is the rejection region?

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.5
Ha:   p   >   0.5 [ANSWER, HYPOTHESES]

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As this is a right tailed test at 0.10 level, the rejection region is

reject Ho when z > 1.281551566. [ANSWER]

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As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.529761905      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.01574852      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.889822365      
          
As z > 1.2816, we REJECT HO.

Thus, there is sufficient evidence to conclude that a majority of American adults disapprove of this government surveillance program. [CONCLUSION]