Harper MTH165 Homework Section 6.6 Latest 2020 MAY

MTH165 ELEMENTARY STATISTICS

Homework Section 6.6

In this section you learned about an amazing result about the sampling distribution of the sample proportion.

All data is either qualitative or quantitative.  In the last section we learned how to make probability computations and use them to make inferential decisions using ___ ________________ data and the random variable ___.  In this section we will learn how to make probability computations and use them to make inferential decisions using _____ _____________ data and the random variable ____.

Turn to page 222 and fill in the following formulas:

μ_p ? =________ and σ_p ? = _________________

                If a sample of size n is taken from a population with a population proportion, p, then the distribution of p ? is approximately normal if the following conditions are met:

1.            ___ ____________ and __ _________________                                                         

2.            ________________

Fill in the following as you work through your given problems in MyOpenMath.

1.            Given:  ____ = _______ and ____ = _______

a.            Given:  n = ____

Check conditions:

1.            np =1.41 which  <10        2.            n (1-p)  = 45.59 which >= 10         3. N = 27000  which >= 940

Can you say the shape of the sampling distribution of the proportion is approx. normal?  Yes No

Why or why not? _____since the first condition did not check out_________________________________________________________

b.            Given:  n = ____

Check conditions:

1.            np=42.3                which >=10                                                                                                         2.            n (1-p)  =4.7 which <10 

Can you say the shape of the sampling distribution of the proportion is approx. normal?  Yes No               Why or why not? _____ since the second condition did not check out_________________________________________________________

c.             Given:  n = __500___                    

Check conditions:

1.np=15                which >=10         2.            n (1-p)  =485  which >=10             3.N = 27000  which >=10000

Can you say the shape of the sampling distribution of the proportion is approx. normal?  Yes No

Why or why not? _________ since all 3 conditions check out_____________________________________________________

d.            Given:  n = _____ and N = ______

Check conditions:

1.np=15which >=10         2.            n (1-p)  =485  which >=10             3. N = 9235  which < 10000

Can you say the shape of the sampling distribution of the proportion is approx. normal?  Yes No

Why or why not? _______ because the third condition did not check out_______________________________________________________

e.            __________ The variable information collected from each individual is now qualitative instead of quantitative_________________________________________________________________________

2.            Given info with correct symbols:  ___p_ = _______                        __n___ = ________

a.            Fill in the following in the context of this problem:

Individual: ____ a randomly selected booked passenger____________________________________________________               

Variable: _____ whether or not a randomly selected booked passenger shows up on time for their flight____________________________________________________

Type of variable:  qualitative                       quantitative-discrete                     quantitative-continuous

rv X = ___ the number of 220 randomly selected booked passengers that show up on time for their flight____________________________________________________________

rvp ? = ____ the percentage of 220 randomly selected booked passengers that show up on time for their flight__________________________________________________________

b.            Check conditions:

1.np =187 which is >= 10               2.n (1-p)= 33 which is >=10          3.N = 1000000 which is  (or assumed to be ) >= 4400

Can you say the shape of the sampling distribution of the proportion is approx. normal?  Yes No

Why or why not? ____all the three conditions are satisfied__________________________________________________________

c.             P(  p? ≥ 0.9          ) = __________________________________________ ≈ ___

d.            Is _____% an unusually high sample percentage?  Since P(    p? ≤ 82%             ) = 0.1063____________

which is ______>________, _% (is/is not) an unusually high sample percentage.

What might you conclude if you see a sample percentage this high?

_______ There is no evidence that the percentage of all booked passengers that show up on time for their flight has changed from 85%_________________________________________________________________________

e.            Is _____% an unusually high sample percentage?  Since P(  p? ≤ 78%               ) = ____________

which is __ ≤____________, ___% (is/is not) an unusually high sample percentage.

What might you conclude if you see a sample percentage this high?

______________ There is evidence that the percentage of all booked passengers that show up on time for their flight is now lower than 85%__________________________________________________________________

3.            Given info with correct symbols:  _____ = _______                        __n___ = _______

a.            Fill in the following in the context of this problem:

Individual: ________ a randomly selected college student________________________________________________               

Variable: _________ whether or not a randomly selected college student is left-handed________________________________________________

Type of variable:  qualitative                       quantitative-discrete                     quantitative-continuous

rv X = ____________ the number of 221 randomly selected college students that are left-handed___________________________________________________

rvp ? = _______ the percentage of 221 randomly selected college students that are left-handed_______________________________________________________

b.            Check conditions:

1.np = 24.31 which is ≥ 10             2.n(1-p) = 196.69 which is ≥ 10    3. N = 5525 which is (or is assumed to be) ≥ 4420

Can you say the shape of the sampling distribution of the proportion is approx. normal?  Yes No

Why or why not? ______because all the three _________conditions are satisfied_______________________________________________

c.             P(  p? ≤ 0.09         ) = __________________________________________ ≈ __

d.            Is ______% an unusually low sample percentage?  Since P(   p? ≤  9%            ) = __________

which is _____________, ___% (is/is not) an unusually low sample percentage.

What might you conclude if you see a sample percentage this low?

There is no evidence that the percentage of all college students that are left-handed is now lower than 11%

e.            Is ______% an unusually low sample percentage?  Since P(   p? ≤ 5% )               = ___________

which is _____________,___% (is/is not) an unusually low sample percentage.

What might you conclude if you see a sample percentage this low?

There is evidence that the percentage of all college students that are left-handed is now lower than 11%