Question

Melanoma is a rare form of skin cancer that accounts for the at majority of skin cancer fatalities. Ultraviolet (UV) exposure is a major risk factor for melanoma, Some body parts are regularly more exposed to the sun than others. Would this be reflected in the distribution of melanoma locations on the body in a population? A random sample of 310 women diagnosed with melanoma was classified according to the known locations of the melanomas on their bodies. Here are the results

Location Head/neck 45, Trunk 80, Upper limbs 34, Lower limbs Count 151

Assuming that these 4 body parts represent roughly equal skin areas, do the data support the hypothesis that melanoma occurs evenly on the body?

A)Explain why a Chi-Squared test is used in this problem.

B) What are the null and alternative hypotheses? Ho: Ha:

C) What is the expected count for each category?

Answer 1

Solution:

Part A) Explain why a Chi-Squared test is used in this problem.

Chi-square test of goodness of fit is used to see how the observed counts are significantly different from expected counts.

Since we would like to test if the distribution of melanoma locations on the body in a population is fitted with expected distribution that melanoma occurs evenly on the body.
Thus in this problem, we use Chi-square test of goodness of fit.

Part B) What are the null and alternative hypotheses?

For Chi-square test of goodness of fit, null and alternative hypotheses are as:

H0: The observed data is consistent with a specified distribution

Vs

Ha:The observed data is not consistent with a specified distribution

Thus for this problem:

H0: Melanoma occurs evenly on the body

Vs

Ha: Melanoma does not occurs evenly on the body

Part C) What is the expected count for each category?

Under null hypothesis H0, Melanoma occurs evenly on the body , then expected count for each Body part is equal and it is given by:

Expected Count = N / k

Expected Count = 310 / 4

Expected Count = 77.5

Thus Expected Counts for each category = 77.5