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In a survey of 1000 people, 700 people said that they voted in the last presidential election. Let p denote the proportion of all people who voted. Find a point estimate for p and also construct a 90% confidence interval for p.
a) 0.700, (0.676, 0.724)
b) 700, (0.676,0.724)
c) 700, (0.642,0.767)
d) 0.700, (0.642,0.767)
e) 0.300, (0.276, 0.324)

Respuesta :

JeanaShupp

Answer: a) a) 0.700, (0.676, 0.724)

Step-by-step explanation:

Confidence interval for population proportion p :

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]\hat{p}[/tex] = Sample proportion, n= sample size, z* = Critical value.

Let p denote the proportion of all people who voted.

As per given, n= 1000

[tex]\hat{p}=\dfrac{700}{1000}\\\\=0.7[/tex]

z* for 90% confidence = 1.645

Required confidence interval :

[tex]0.7\pm (1.645)\sqrt{\dfrac{0.7(1-0.7)}{1000}}\\\\=0.7\pm(1.645)\sqrt{0.00021}\\\\=0.7\pm (1.645)(0.0145)\\\\=0.7\pm 0.0238525\\\\=(0.7-0.0238525,0.7+0.0238525)\\\\=(0.6761475,\ 0.7238525)\approx(0.676, 0.724)[/tex]

hence, the correct option is a) a) 0.700, (0.676, 0.724)

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