60 patients survive five years Test the hypothesis that the

60 patients survive five years. Test the hypothesis that the US study has the same survival rate claimed by the French. Use a two-sided test at the 5% level of significance. (3 points) 4. Audiogram hearing tests were examined for six rock musicians. Test results from before they became musicians were compared to results from five years afterwards. The decibel readings (dB) at 1000 Hz frequency appear in the table below. Test the hypothesis of no difference in decibel readings against the alternative that decibel readings have increased (which would indicate hearing loss). Use a 5% level of significance. (4 points) 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

Solution

We use paired t test to do it because it tests the same subjects twice

Let mu_dbar be the mean difference between before and after

The test hypothesis:

Ho: mu_dbar=0 (i.e. null hypothesis)

Ha: mu_dbar<0 (i.e. alternative hypothesis)

The test statistic is

t=mean difference/(s/vn)

=-2.43

The degree of freedom =n-1=6-1=5

It is a left-tailed test.

Given a=0.05, the critical value is t(0.05, df=5) =-2.02 (from student t table)

The rejection region is if t<-2.02, we reject Ho.

Since t=-2.43 is less than -2.02, we reject Ho.

So we can conclude that decibel readings have increased

41.667	mean Before
44.833	mean After
-3.167	mean difference (Before - After)
3.189	std. dev.
1.302	std. error
6	n
5	df