Current data provided by the 2010 census indicates that the prevalence of breast
ID: 3366381 • Letter: C
Question
Current data provided by the 2010 census indicates that the prevalence of breast cancer in the US is still on the rise, while the mortality rates have slightly declined over time. A researcher at a local health department conducts an observational study to determine the prevalence in the particular region. The researcher gathers 2,168 participants and confirms 246 cases of breast cancer in her sample. The census data indicates a national prevalence of 23.5%. Do you feel that the breast cancer prevalence is more in the region of investigation compared to the national figure? Justify your answer with statistical reasoning.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.235
Alternative hypothesis: P > 0.235
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).
S.D = sqrt[ P * ( 1 - P ) / n ]
S.D = 0.00911
z = (p - P) / S.D
z = - 13.34
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a one-tailed test, the P-value is the probability that the z-score is greater than -13.34
Thus, the P-value = 0.9999.
Interpret results. Since the P-value (almost 1) is greater than the significance level (0.05), we have to accept the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that breast cancer prevalance is more in the region of investigation compared to the national figure.
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