According to a Gallup poll conducted in 2008, 78.3% of Americans felt satisfied

Question

According to a Gallup poll conducted in 2008, 78.3% of Americans felt satisfied with the way things were going in their personal lives. A researcher wonders of the percentage satisfied is different today. To find out, the researcher surveys a random sample of 1,173 Americans, and finds that 892 feel satisfied with the way things are going in their personal lives. The researcher wishes to test the null hypothesis at a significance level of .05. (a) Conduct a large sample z test to determine whether there is sufficient evidence to reject the null hypothesis. Should you do a one-tailed test or a two-tailed test? (b) Interpret the meaning of the results in the context of this study

Explanation / Answer

a)

As it said "wonders if the percentage satisfied is DIFFERENT today", then it is a two tailed test (it doesn't matter if it's greater or less).

[ANSWER: TWO TAILED TEST]

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Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.783
Ha:   p   =/=   0.783

As we see, the hypothesized po =   0.783      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.760443308      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.012035434      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.874190242      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.060904209      

significance level =    0.05      

As P > 0.05 we   FAIL TO REJECT THE NULL HYPOTHESIS.  

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b)

Hence, there is no significant evidence at 0.05 level that the percentage of those who are satisfied today is different from the percentage in 2008. [CONCLUSION]

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