Harper MTH165 Homework Section 6.5 Latest 2020 MAY

MTH165 ELEMENTARY STATISTICS

Homework Section 6.5

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.            ___  ___ = _____ _ __________ = _________________ = ______________

symbol                 formula without numbers                            formula with numbers                                                   value    

___ ? ___ = _______________ = ________________ = ______________

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                     ___ ___ = _______________ = ________________ = _____________

symbol                 formula without numbers                            formula with numbers                                                   rounded value

 

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.            __ ____ = ______________ = _________________ = ______________

symbol                 formula without numbers                            formula with numbers                                                   value    

___σ_x ? ___ = _______________ = _________________ = _____________

symbol                 formula without numbers                            formula with numbers                                                   rounded value

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_____              

symbol                 formula without numbers            formula with numbers   value     units

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?