10 test Compute the PValue Comparing scales In an experiment

10 test

Compute the P-Value

Comparing scales: In an experiment to determine whether there is a systematic difference between the weights obtained with two different scales. 10 rock specimens were weighed, in grams, on each scale. The following data were obtained: Let mu 1 represent the mean weight on Scale 1 and mu d= mu 1- mu 2. Can you conclude that the mean weight on Scale 1 is less the mean weight on Scale 2? Use the a = 0.05 level of significance and the TI-8- calculator to answer the following.

Solution

The test hypothesis:

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

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

The test statistic is

t=mean difference/(std. dev./vn)

=-0.222/(1.24517/sqrt(10))

=-0.56

It is a one-tailed test

The degree of freedom =n-1=10-1=9

So the p-value= P(t with df=9 <-0.56) =0.2946 (from student t table)

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

So we can not conclude that the mean weight on Scale 1 is less than mean weight on Scale2

14.24700	mean Scale 1
14.46900	mean Scale 2
-0.22200	mean difference (Scale 1 - Scale 2)
1.24517	std. dev.
0.39376	std. error
10	n
9	df