In this section you learned about the most amazing result about the sampling distribution of the sample mean.
In this section you learned about the most amazing result about the sampling distribution of the sample mean.
Define sampling distribution:
Define sampling error:
Turn to page 211 and fill in the following formulas:
μ_x ? =μ_x and σ_x ? =
To check if the sampling distribution of the sample mean is normal or at least approximately normal you need to check the following: 1. 2.
Fill in the following as you work through your given problems in MyOpenMath.
1.Given: population distribution (is/is not) normal, _μ= ______ and ____ = ________
a. Given: n = ___
Can you say what the shape of the sampling distribution of the mean is? Yes No
Why or why not? ________________population is not normal
n is less than 30________________________________
b. ___ ___ = _____ _ __________ = _________________ = ______________
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___ ? ___ = _______________ = ________________ = ______________
symbol formula without numbers formula with numbers rounded value
c. Given: n = ___
Can you say what the shape of the sampling distribution of the mean is? Yes No
Why or why not? ________is known
n is a at least 30_________________________________________________________
d. ____ = _____________ = __________________ = _______________
symbol formula without numbers formula with numbers value ___ ___ = _______________ = ________________ = _____________
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2. Given: population distribution (is/is not) normal, ___μ_ = ______ and _____ = _______
a. Given: n = ___
Can you say what the shape of the sampling distribution of the mean is? Yes No
Why or why not? _________________σ_is known
population is normal_________________________________________________
b. __ ____ = ______________ = _________________ = ______________
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___σ_x ? ___ = _______________ = _________________ = _____________
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3.a. Fill in the following in the context of this problem:
Individual: _______a randomly selected Atlantic code________________________________________________________
Variable: _the length__________________________________________________________
Type of variable: qualitative quantitative-discrete quantitative-continuous
rv X = the length of a randomly selected Atlantic code_______________________________________________________
b. Given info: normal pop? yes/no μ__ = ___ __cm __σ = _ cm n__ = _
c. rv = ______________the mean length of randomly selected Atlantic cod_______________________________________________________
d. ______ = _______________ = _________________ = _______ ________cm_____
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e. ____ = __________ = __________________ = ___________ _________cm____
symbol formula without numbers formula with numbers rounded value unit
f. The sampling distribution of the mean is ___normal or approximately normal because __σ__is known and population is normal___________________________________________________________________
g. P( X ?< 48.9 ) = ________________________________________ ______________ (4 dec pl)
h. P( X ?>52.87 ) = ________________________________________ ______________ (4 dec pl)
i. Is _____ cm unusually long? Yes No Why or why not? _______________the probability of having a sample mean length of at least 52.87 cm is less than or equal to 0.05______________
j. What might you conclude if a sample had a mean was as high as the one in part i?
_________There is evidence that the mean length of all Atlantic cod may now be higher than 49.9 cm__________________________________________________________________________
4.a. Fill in the following in the context of this problem:
Individual: _______a randomly selected male in the US age 40 to 49________________________________________________________
Variable: ______the fat consumption___________________________________________________________
Type of variable: qualitative quantitative-discrete quantitative-continuous
rv X = the ______________________________________________________________________
b.Given info: normal pop? yes/no _μ_ = ___ _σ_ = ______ __ _n_ = ______
c. rv = _________the fat consumption of a randomly selected male in the US age 40 to 49_______________________________________________________________
d. ___ = _______ = __________________ = _______________________
symbol formula without numbers formula with numbers value units
e. ___σ_x ? ___ = ______ __________ = __________________ = ______________ __________g_____
symbol formula without numbers formula with numbers rounded value units
f. The sampling distribution of the mean is ______normal or approximately normal
n is at least 30____________________________________________________________________
g. P( X ?< 101.9 ) = ______________ ____________________________ ______________ (4 dec pl)
h. P( X ?<101.5 ) = __________________________________ ______________ (4 dec pl)
i. Is ___101.5___ g unusually low? Yes No Why or why not? _____ the probability of having a sample mean fat consumption of at most 101.5 g is less than or equal to 0.05________________________
j. What might you conclude if a sample had a mean was as low as the one in part i?
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