6 A ichthyologist measured the adult body weight of two grou

6. A ichthyologist measured the adult body weight of two groups of fish: one group containing external parasites and another healthy group. The ni = 34 parasitized fish had a mean body weight of x1 vector = 194 g and a standard deviation of si = 33 g. whereas the 112 38 healthy fish yielded ?x2 vector = 211 g and S2 25 g. Test the hypothesis of no dit1rence in body weight between parasitized and healthy fish versus the alternative that the parasitized fish arc smaller. Use a 1% level of significance. (3 points)

Solution

Let mu1 be the population mean for parasitized fish

Let mu2 be the population mean for healthy fish

The test hypothesis:

Ho: mu1=mu2 (i.e. null hypothesis)

Ha: mu1 < mu2 (i.e. alternative hypothesis)

The test statistic is

t=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(194-211)/sqrt(33^2/34+25^2/38)

=-2.44

It is a left-tailed test.

Given a=0.01, the critical value is Z(0.01) =-2.33 (from standard normal table)

The rejection region is if Z<-2.33, we reject Ho.

Since Z=-2.44 is less than -2.33, we reject Ho.

So we can conclude that the parasitized fish are smaller