The proportion of baby boys born in the United States has hi

The proportion of baby boys born in the United States has historically been 0.51. You choose an SRS of 45 newborn babies and find that 42% are boys. Do ALL calculations to 5 decimal places before rounding.

(a) In the list below, select all that apply. The number 0.51 is a

a.Statistic

b.Parameter

c.Sample mean

d.Population mean

e.Sample proportion

f.Population proportion

(b) In the list below, select all that apply. The number 0.42 is a

a.Statistic

b.Parameter

c.Sample mean

d.Population mean

e.Sample proportion

f.Population proportion

(c) If you take samples of 45 newborns many times, the sampling distribution of the sample proportion of boys will be

e.The sample size is too small to say what the distribution of the sample proportion is

Solution

a)

OPTION B: PARAMETER (since it is a population)
OPTION F: POPULATION PROPORTION (as it is a percentage)

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b)

OPTION A: STATISTIC (since it is from a sample)
OPTION E: SAMPLE PROPORTION (as it is a percentage from a sample)

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C)

Here,  
n =    45
p =    0.51

Hence,

u = mean = p =    0.51
  
s = standard deviation = sqrt(p(1-p)/n) =    0.074520691

Thus,

OPTION D: p^ ~ N(0.51, 0.07452) [we choose p^ because it is a distirbution of sample proportions]

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d)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.42      
u = mean = p =    0.51      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.074520691      
          
Thus,          
          
z = (x - u) / s =    -1.207718276      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.207718276   ) =    0.113577823 [ANSWER]