Question

We wish to test the null hypothesis that the left foreleg and left hind leg lengths of deer are equal. We obtain the following statistics :

D bar= 3.34 cm

standard area of d- bar = 4

n= 16

Do these data provide sufficient evidence to indicate that the left foreleg of the deer is different in size from the left hind leg? Let ?=0.05.

8. What is the null hypothesis?

9. What is the alternative hypothesis?

10. What is the test statistic used?

11. What is the calculated test statistic?

12. What is the critical value of the test statistic

13. What is the p-value?

14. What is the statistical decision?

Answer 1

Here we have given that

Claim: To check wheter the left foreleg of the deer is different in size from the left hind leg or not.

The Hypothesis is

$Ho: \mu d=0$

v/s

$H1: \mu d \neq 0$

Now,

n= Number of observation =16

$\bar d$ = sample mean of differences = 3.34  

Sd= sample standard deviation of differences = 4

Now, we can find the test statistic

$Tstat= \frac{\bar d- \mu d}{\frac{sd}{\sqrt(n)}}$

=$\frac{ 3.34}{\frac{4}{\sqrt(16)}}$

=3.34

Now, we want to find the critial value

Degrees of freedom = n-1= 16-1=15

$\alpha$= level of significance=0.05

tcritical = 2.131

Now, we can find the P-value

P-value =0.0045 ( using EXCEL =TDIST(x,D.F,tail))

Decision:

P-value < 0.05 ($\alpha$)

Conclusion:

That is we reject Ho (Null Hypothesis) it means that there is sufficient evidence that the left foreleg of the deer is different in size from the left hind leg