In this section you learned about the most amazing result about the sampling distribution of the sample mean.
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Get it written →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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