Respuesta :
Answer:
There is not enough statistical evidence to conclude that the cumulative incidence of prostrate cancer among 50-year old men differs from that of 70-year old men
Step-by-step explanation:
The population 10 year cumulative incidence of prostrate cancer among 70 year old men, p = 0.06
The number of 50 year old men in the sample, n = 260 men
The number of the sampled men that developed prostrate cancer = 13 men
The significance level, α = 0.05
Let the null hypothesis, H₀: [tex]\hat{p}[/tex] = p
The alternative hypothesis, Hₐ: [tex]\hat{p}[/tex] ≠ p
The standard score, [tex]z_{\alpha /2}[/tex] = 1.96
The test statistic, 'z', is given as follows;
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p \cdot q}{n}}}[/tex]
[tex]\hat{p}[/tex] = 13/260 = 0.05
q = 1 - p = 1 - 0.06 = 0.94
[tex]Therefore, \ z=\dfrac{0.05-0.06}{\sqrt{\dfrac{0.06 \times 0.94}{260}}} = \dfrac{\sqrt{9165} }{141} \approx -0.68[/tex]
From the z-table, we find the p-value as follows;
P(z ≈ -0.68) = 0.24825
Therefore, given that the p-value, 0.24825 is larger than the significance level, α/2 = 0.025, we fail to reject the null hypothesis, and therefore, there is not enough statistical evidence to conclude that the cumulative incidence of prostrate cancer among 50-year old men differs from that of 70-year old men
