Question

The average adult giraffe is 17 feet tall. After a couple of years of horrible drought and famine in a particular area, an animal specialist thinks that the average height of adult giraffe is now shorter than the assumed average.

a) What is this animal specialist's null and alternative hypothesizes?

b) The animal specialist measured 37 giraffes; their average height was 15.8 feet and their standard deviation was 1.1 feet. Test the biologist’s claim at the α= 0.01 level.

What is the critical value?

c) The animal specialist measured 37 giraffes; their average height was 15.8 feet and their standard deviation was 1.1 feet. Test the biologist’s claim at the α= 0.01 level.

Make and justify a statistical decision at 0.01 level, and state your conclusions in context of the problem.

Answer 1

The average adult giraffe height , = 17 feet

a) Null hypothesis, H0 :   = 17

Alternate hypothesis, HA: < 17 ( left tailed test) ; claim

b) Sample size, n= 37

Sample height, = 15.8

Sample standard deviation, s= 1.1  

Since the population standard deviation is missing, so we will using one sample t-test

   Critical value , t( 37-1, 0.01) = - 2.434

c) Sample size, n= 37

Sample height, = 15.8

Sample standard deviation, s= 1.1  

Test statistics= = = -6.6357

Since the Test statistic is less than the critical value . That means that the test statistics lies in the critical region. Hence we will reject the null hypothesis.

   Thus we have enough evidence to support the biologists claim that the average height of adult giraffe is now shorter than the assumed average.