Use the following scenario and data for all the questions s a large city,the pop

Question

Use the following scenario and data for all the questions s a large city,the popaliation proportion of residents favoring a specific candidate for the prohate coujudgeis p-035. A randoen sample of -81 residents is selected.Use pto denote the sample proportion of residents favoring this specific candidane probate court judge is p-0.35. A random sample of n-3 1 residents is selected. Use ·to denote the sample The mean (or expected value) of the sample peopertion p is 0.0630 00028 0.0389 0.6500 none of the above QUESTION 2 1 points Save Answer The standard deviation of the sample proportion p is closest to 0.0530 0.0028 0.0389 0.6500 none of the above

Explanation / Answer

1.

The mean of p^ is p, then

OPTION B: 0.3500 [ANSWER, NONE OF THE ABOVE]

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2.

Also, as n = 81, p = 0.35,

s = standard deviation = sqrt(p(1-p)/n) =    0.052996622 = 0.0530 [ANSWER, A]

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3.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.3      
u = mean = p =    0.35      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.052996622      
          
Thus,          
          
z = (x - u) / s =    -0.943456353      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.943456353   ) =    0.172723765 --> 0.1736 [ANSWER, D]

[Note that this is an exact answer, so the small difference would be due to rounding off by your professor.]

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4.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.38      
u = mean = p =    0.35      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.052996622      
          
Thus,          
          
z = (x - u) / s =    0.566073812      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.566073812   ) =    0.285671802-->0.2843 [ANSWER, D]

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5.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.28      
u = mean = p =    0.35      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.052996622      
          
Thus,          
          
z = (x - u) / s =    -1.320838894      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1.320838894   ) =    0.906722456-->0.9066 [ANSWER, A]

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