Arandom sample of 500 registered voters in phoenix is asked if they favor the use of oxygenated fuels year-round to reduce air pollution. if more than 314 voters respond positively, we will conclude that at least 60% of the voters favor the use of these fuels. round your answers to four decimal places (e. g. 98.7654).

a) find the probability of type i error if exactly 60% of the voters favor the use of these fuelsb) what is the type ii error probability (beta) β if 75% of the voters favor this action?

a) 0.0853

b) 0.0000

Step-by-step explanation:

Parameters given stated that;

H₀ : p = 0.6

H₁ : p  = 0.6, this explains the acceptance region as;

p° ≤ =0.63 and the region region as p°>0.63 (where p° is known as the sample proportion)

a).

the probability of type I error if exactly 60% is calculated as :

∝ = P (Reject H₀ | H₀ is true)

   = P (p°>0.63 | p=0.6)

where p° is represented as pI in the subsequent calculated steps below

    = P  

    = P  

    = P  

    = P   [Z > 1.37]

    = 1 - P   [Z ≤ 1.37]

    = 1 - Ф (1.37)

    = 1 - 0.914657 ( from Cumulative Standard Normal Distribution Table)

    ≅ 0.0853

b)

The probability of Type II error β is stated as:

β = P (Accept H₀ | H₁ is true)

  = P [p° ≤ 0.63 | p = 0.75]

where p° is represented as pI in the subsequent calculated steps below

  = P

  = P

  = P

  = P [Z ≤ -6.20]

  = Ф (-6.20)

  ≅ 0.0000 (from Cumulative Standard Normal Distribution Table).

a

step-by-step explanation:

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correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,