Question

Suppose the mean weight of King Penguins found in an Antarctic colony last year was 15.3 kg. In a sample of 16 penguins this year in the same colony, the mean penguin weight is 14. 3 kg. Assume the sample standard deviation is 2.7kg. Perform a hypothesis test at the α = 0.05 significance level to see if the mean weight of King Penguins has gone down this year.Use H0: μ = 15.3 Ha: μ < 15.3

a)What is the test statistic for this sample (use at least 3 decimal places)?

b) What is the p-value for this sample? (use Statcrunch)

c)Evaluate the strength of the evidence and state the conclusion (in the context of this question).

Answer 1

a) The test statistic here is computed as:

Therefore -1.481 is the required test statistic value here.

b) As we are testing here whether the mean is less than 15.3, therefore the p-value here is obtained from the t distribution tables as:

p = P( t16-1 < -1.481) = 0.0796

Therefore 0.0796 is the required p-value here.

c) As the p-value here is 0.0796 > 0.05 which is the level of significance, therefore the test is not significant here at the 5% level of significance and therefore we dont have sufficient evidence here that the mean is less than 15.3