Tests for 1-sample data

Tests for 1-sample Data

The following data gives the additional hours of sleep for 10 patients given $l$%-hyoscyamine hydrobromide.

    read c1
    1.9
    0.8
    1.1
    ...
    3.4

    end
    name c1='SLEEP'

Question 1: Does the l-isomer prolong sleep? Perform a test of H0: mu =0 versus H1: mu >0 at a alpha=0.0 significance level.

Minitab will do the test for you if you know how to use the test command:

 ttest of mu=0 on 'SLEEP';
 alternative=1.

The subcommand alternative=1 tells Minitab that H1 is of the form mu > mu0. (Use -1 for a left sided alternative and 0 for an alternative of the type mu <> mu0).

Minitab will actually not do all the work for you. Minitab will only report the P-value. The P-value gives the area to the right of the observed t-statistic (i.e. the statistic

             _
	t = (x-mu)/(s/sqrt(n))

If for example P=0.03 then for alpha = 0.05> the conclusion would be ``reject H0'' because the observed t-statistic lies beyond the cutoff for a 0.05 right tail (smaller tail area means greater t -- why?). If however alpha=0.01 then the conclusion would be ``fail to reject'' because the observed t-value lies still to the left of the 99-th percentile which cuts off a 0.01 right tail.

Qustion 2: What is the reported P-value?

Question 3: For a two sided test: H0: mu=0 versus H1: mu <> m0 at alpha=0.01, what would be your decision? Why?