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In 1965, about 44% of the U.S. adult population had never smoked cigarettes. A n

ID: 3133086 • Letter: I

Question

In 1965, about 44% of the U.S. adult population had never smoked cigarettes. A national health survey of 1472 U.S. adults (presumably selected randomly) during 2010 revealed that 677 had never smoked cigarettes. Suppose you wished to test whether there has been a change since 1965 in the proportion of U.S. adults who have never smoked cigarettes. You test the hypotheses H0: p = 0.44, Ha: p > 0.44. The P-value of the test is

A. greater than 0.10.

B. between 0.05 and 0.10

. C. between 0.01 and 0.05.

D. below 0.01.

Explanation / Answer

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.44
Ha:   p   >   0.44
As we see, the hypothesized po =   0.44      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.459918478      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.012937979      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.539535505      
          
As this is a    1   tailed test, then, getting the p value,  

OPTION B: B. between 0.05 and 0.10 [ANSWER]
          
[Actually, it is more exactly p =    0.061836808]