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]