4. The NCHS report indicated that in 2002 the prevalence of cigarette smoking among American adults was 21.1%. Data on prevalent smoking in n=3,536 participants who attended the seventh examination of the Offspring in the Framingham Heart Study indicated that 482 of the respondents were currently smoking at the time of the exam. Suppose we want to assess whether the prevalence of smoking is lower in the Framingham Offspring sample given the focus on cardiovascular health in that community. At a 5% significance level, is there evidence of a statistically lower prevalence of smoking in the Framingham Offspring study as compared to the prevalence among all Americans?
The hypothesis being tested is:
H0: p = 0.211
Ha: p < 0.211
Observed | Hypothesized | |
0.1363 | 0.211 | p (as decimal) |
482/3536 | 746/3536 | p (as fraction) |
482. | 746.096 | X |
3536 | 3536 | n |
0.0069 | std. error | |
-10.88 | z | |
0.00E+00 | p-value (one-tailed, lower) |
The p-value is 0.0000.
Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.
Therefore, we can conclude that the prevalence of smoking is lower in the Framingham Offspring sample given the focus on cardiovascular health in that community.
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