1.The Bee Informed Partnership, Apiary Inspectors of American, and the United St
ID: 3135386 • Letter: 1
Question
1.The Bee Informed Partnership, Apiary Inspectors of American, and the United States Department of Agriculture estimated that 23.1% of all bee colonies in the United States were lost over the 2014/2015 winter.[1] Suppose this estimated percentage is true for all bee colonies in the United States during the 2014/2015 winter.
a)What is the population?
b)What is the parameter? Describe it in words and provide the value of the parameter.
c)What is the statistic? Describe it in words.
d)Suppose we would like to examine random samples of 20 bee colonies in the United States during the 2014/2015 winter. Describe the sampling distribution of the proportion of bee colonies that were lost. Make sure to check the appropriate conditions and describe the mean, standard deviation, and shape.
e)Suppose we would like to examine random samples of 100 bee colonies in the United States during the 2014/2015 winter. Describe the sampling distribution of the proportion of bee colonies that were lost.
f)In a random sample of 100 bee colonies in the United States during the 2014/2015 winter, 30 were lost. Is this an unusually large number of bee colonies lost? Explain.
g)In a random sample of 100 bee colonies in the United States during the 2014/2015 winter, 40 were lost. Is this an unusually large number of bee colonies lost? Explain.
[1] https://beeinformed.org/results/colony-loss-2014-2015-preliminary-results/
Explanation / Answer
a) Population is the entire pool from which a statistical sample is drawn. here bee colonies are population.
b)here parameter of interest is p, the proportion of bee colonies in the United States were lost =23.1%
c) sample value is called statistic. A statistic is a single measure of some attribute of a sample (e.g., its arithmetic mean value). It is calculated by applying a function (statistical algorithm) to the values of the items of the sample, which are known together as a set of data.
d) here sampling distribution will be binomial with n=20 and p=0.231
mean=n*p=20*0.231=0.462
variance=p((1-p)/n=0.231*(1-0.231)/20=0.0089
standard deviation=sqrt(variance)=0.094
e)here also sampling distribution will be binomial with n=100, p=0.231
f) n=100, p=0.231, P=0.3 ,n=100 we calculate z=(P-p)/SE(p)=(0.3-0.231)/0.0018=38
it is statistically larger number of colony lost as the critical z at 5% level of significance is 1.96
g) n=100, p=0.231, P=0.4 ,n=100 we calculate z=(P-p)/SE(p)=(0.4-0.231)/0.0018=93
it is statistically larger number of colony lost as the critical z at 5% level of significance is 1.96
which is less than 1.96 , so it is not less
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