5 A botanist measured the heights of plants grown in a high

5. A botanist measured the heights of plants grown in a high ozone chamber versus a control group. The data are presented below. Test the hypothesis of no difference in the height versus the alternative of a difference at the 5% level of significance. (4 points) Plant Height (cm) High Ozone Control 6. A ichthyologist measured the adult body weight of two groups of fish: one group containing external parasites and another healthy group. The m = 34 parasitized fish had a mean body weight of x1 = 194 g and a standard deviation of s1 = 33 g, whereas the n2 = 38 healthy fish

Solution

Let mu1 be the population mean for high ozone

Let mu2 be the population mean for control

The test hypothesis:

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

Ha: mu1 not equal to mu2 (i.e. alternative hypothesis)

The test statistic is

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

=(94-118.6)/sqrt(13.45^2/6+19.22^2/5)

=-2.41

It is a two-tailed test.

The degree of freedom =n1+n2-2=6+5-2=9

Given a=0.05, the critical values are t(0.025, df=9) =-2.26 or 2.26 (from student t table)

The rejection regions are if t<-2.26 or t>2.26, we reject Ho.

Since t=-2.41 is less than -2.26, we reject Ho.

So we can conclude that there is a difference.

High Ozone	Control
94.00	118.60	mean
13.45	19.22	std. dev.
6	5	n