Related questions
Historical records show that these dolphins had an average mass of 80 kg in the early days of settlement on the Islands. However, there are concerns that depletion of prey species has caused the average mass to drop in the last 300 years. Researchers from Hofn University conducted a survey of this dusky dolphin population to look for evidence of a decrease in mass.
a)Concerned about the assumptions for their t test, the researchers decided to carry out a test using the Binomial distribution to determine if dusky dolphins tend to have masses less than 80 kg. To do this, they test H0:p=0.5 against H1:p>0.5. Here p would be
the
the probability of a dusky dolphin having a mass greater than 76.2 kg
the probability of a dusky dolphin having a mass not equal to 80 kg
the probability of a dusky dolphin having a mass less than 80 kg
b)The researchers observed that 8 of the 12 dolphins had a mass less than 80 kg. The p-value from the Binomial distribution of whether dusky dolphin mass is less than 80 kg is
0.1208
0.1938
0.3877
0.8062
c)
In a sample of size 12, what is the minimum number of dusky dolphins with masses less than 80 kg that would need to be observed to give significant evidence at the 5% level?
8
9
10
12
d)
Suppose that the true probability of a dusky dolphin having mass less than 80 kg is 85%. What is the power of the test in Question 7 to detect the decrease at the 5% level, using a sample of 12 dolphins?
0.2642
0.5887
0.7358
0.8500
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