Question

From previous studies, it has been generally believed that Northern Hemisphere icebergs have a mean depth of 270 meters. An environmentalist has suggested that global warming has caused icebergs to have greater depth. A team of scientists visiting the Northern Hemisphere observed a random sample of 41 icebergs. The depth of the base of the iceberg below the surface was carefully measured for each. The sample mean and standard deviation were calculated to be 276 meters and 20 meters respectively.

Part e) Assume all necessary conditions are met (random sampling, independence samples, large enough sample size). Which of the following approximate the sampling distribution of the test statistic in Part d:
Normal distribution
t-distribution

Part f) In which of the following ranges must the P-value must lie?[You will need the t-table to answer this question.]

A. <0.005
B. 0.05-0.01
C. 0.01-0.025
D. 0.025-0.05
E. 0.05-0.10
F. >0.10

Part g) Based on the PP-value that was obtained, you would (Select all that apply):

A. fail to reject the null hypothesis at all.
B. neither reject nor accept the null hypothesis.
C. reject the null hypothesis at α=0.1α=0.1 level of significance
D. reject the null hypothesis at α=0.05α=0.05 level of significance
E. believe the null hypothesis is true.
F. None of the above

Answer 1

To Test :-

H0 :- µ = 270
H1 :- µ > 270

Part e)

We will use t distribution.

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 276 - 270 ) / ( 20 / √(41) )
t = 1.9209

Part f)

P - value = P ( t > 1.9209 ) = 0.0309

D. 0.025-0.05

part g)

Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.0309 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

Reject null hypothesis if P value < α = 0.1 level of significance
P - value = 0.0309 < 0.1 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

C. reject the null hypothesis at α=0.1α=0.1 level of significance
D. reject the null hypothesis at α=0.05α=0.05 level of significance