In 5, about 44% of the U.S. adult population had never smoked cigarettes. A nati
ID: 3256258 • Letter: I
Question
In 5, 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 H_0: p = 0.44, H_a: p notequalto 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
Null and Alternative Hypothesis:
Ho: p = 0.44
Ha: p ¹ 0.44
Test Statistics:
z = (p^ - P)/sqrt ((P*(1-P))/n)
p^ = 677/1472 = 0.4599
z = (0.4599 -0.44)/sqrt ((0.44*(1-0.44))/1472) = 1.54
p-value:
2 * P ( z > 1.54 )
= 2 *P ( z < -1.54 )
By Normal Distribution Table we get,
P ( z < -1.54 ) = 0.0618
Now,
2 * P (z < -1.54 ) = 2 * 0.0618 = 0.1236
So p-value is > 0.10
Answer:
( A ) greater than 0.10