For many years the standard for the mean weight of a newborn African Elephant ha
ID: 3318254 • Letter: F
Question
For many years the standard for the mean weight of a newborn African Elephant has been thought to be 200 pounds. Elephant weights are normally distributed. Has the average weight increased due to global warming? That is the question. Tanya Nap, the elephant ranger in Kruger National Park, randomly selected 15 newborn African elephants and weighed them. The weights in pounds were as follows:
187, 251, 242, 241, 183, 187, 194, 280, 238, 191, 251, 229, 275, 178, 249
Let the true (unknown) mean newborn African elephant weight be with a true (unknown) standard deviation of . We want to see if < 200 pounds.
The null hypothesis is
H0:=200
. We will test this against the alternative
Ha
.
If we conclude that is > 200 then Tanya will get a huge award for finding something good about global warming. This award should be well-deserved (not just lucky) so we do not want to reject
H0
unless we are pretty sure that > 200.
Let x = the sample mean and s = the sample standard deviation.
We want to test at the 3% level.
a) What should the alternative hypothesis,
Ha
, be?
Ha:=3%
Ha:<200
Ha:200
Ha:>200
Ha:=200
b) What is the formula for your test statistic?
T =
T =
T =
T =
T =
c) What value does your test statistic,T, take on with the sample data?
d) Calculate the critical value,tstar, for your test.
e) For what values of your test statistic, T, is the null hypothesis rejected?
T < tstarT > tstar/2 or T < -tstar/2 |T - tstar| < 1.96T > tstar
f) Calculate the p-value for this test.
g) If we ran 10000 3% level tests then about how many times would we make a Type I error?
l) Copy your R script for the above into the text box here.
Explanation / Answer
a) The question mentions two things:-
1. "We want to see if < 200 pounds" means --> Ha: mu < 200
2. "We want to see award Tanya if > 200 pounds" means --> Ha: mu > 200
As per the most relevant of 1. and 2., you can choose your answer accordingly! [Answer]
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b) t-statistic for the test is calculated as: (x - mu)/(sd/sqrt(n)) = (x - 200)/(sd/sqrt(15)) => Option #3 [Answer]
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c) sample_mean = 225.0666667, sample_stdDeviation = 35.0111
With the sample data, value of t-statistic = (225.066667 - 200)/(35.0111/sqrt(15)) = 2.779 [Answer]
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d) tstar for 3% level and DoF = 14 (mean unknown) is: 2.45 (approximately)
FROM T-Table --> LINK: https://www2.palomar.edu/users/rmorrissette/Lectures/Stats/ttests/TTable.jpg
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e) Null hypothesis is rejected if t-statistic is greater than t-star (t-test_statistic > tstar)
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f) p-value for t-test is: 0.007389 [Use LINK: http://www.socscistatistics.com/pvalues/tdistribution.aspx]; single tailed test
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g) Number of Type 1 errors = 10000*(Prob of Type 1 error) = 10000*(1-alpha) = 10000(1-0.97) = 300 Type 1 errors [Answer]
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