Fish from an F1 Hybrid cross of the Genus Xiphophorus platyf

Fish from an F1 Hybrid cross of the Genus Xiphophorus (platyfish and swordtails) are known to get spontaneous melanomas. It has been proposed that the fish get more melanomas if exposed to UV light. A cohort of the 94 fish was exposed to UV light, B region. Twenty-one fish from this cohort developed melanomas by 1 year. A control group of 78 fish were raised and kept under standard florescent lighting. Of these fish 6 developed melanomas by 1 year. Did the UV group have a higher proportion of melanoma?

Solution

p1=21/94 =0.2234043

p2=6/78 =0.07692308

Ho: p1=p2 (i.e. null hypothesis)

Ha: p1>p2 (i.e. alternative hypothesis)

The test statistic is

Z=(p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.2234043-0.07692308)/sqrt(0.2234043*(1-0.2234043)/94+0.07692308*(1-0.07692308)/78)

=2.79

It is a one-tailed test.

Assume that the significant level a=0.05

The critical value is Z(0.05) = 1.645 (from standard normal table)

Since Z=2.79 is larger than 1.645, we reject Ho.

So we can conclude that the UV group has a higher proportion of melanoma