Question

You conduct a thorough literature review and find that 5 out of 320 young adults surveyed had coloncancer in 1995, whereas 35 out of 425 young adults surveyed had colon cancer in 2015. Compute the95% confidence interval for each time period and use this information to determine if there is anyevidence that the prevalence of colon cancer increased from 1995 to 2015.

Answer 1

From standard normal tables, we have:
P( -1.96 < Z < 1.96 ) = 0.95

For young adults in 1995, the sample proportion is computed as:
p = 5/320 = 1/64 = 0.015625

Therefore the confidence interval here is computed as:

This is the required 95% confidence interval for the prevalence of colon cancer in 1995.

Now the same is computed for 2015 is computed here as:
p = 35/425 = 0.0824

This is the required 95% confidence interval for the prevalence of colon cancer in 2015.

As the whole confidence interval in 2015 lies above the upper limit of the confidence interval in 1995, therefore we have sufficient evidence here that the colon cancer prevelance has increased from 1995 to 2015 here.