Question

A random sample of ?=80 in-coming college freshmen showed that 44 were planning to bring a car with them to campus next fall. Suppose that we are interested in forming a confidence interval at 95 percent for the proportion of all in-coming college freshmen who are planning to bring a car to campus next fall.

Where appropriate, express your answer as a proportion (not a percentage). Round answers to three decimal places.

Estimate: _______

Standard error: ________

Multiplier:_________

Answer 1

given data are:-

sample size(n) = 80 , x = 44

a).Estimate be :-

$\hat{p}=\frac{x}{n}=\frac{44}{80}\approx \mathbf{0.55}$

b). The Standard error be:-

$SE=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\sqrt{\frac{0.55(1-0.55)}{80}}\approx 0.056$

c). the multiplier (z critical value for 95 % confidence level) be:-

$z^*=1.96$

the 95% confidence interval for the proportion of all in-coming college freshmen who are planning to bring a car to campus next fall be:-

$=\hat{p}\pm z^**SE$

0.55 + (1.96 +0.056)

$\approx \mathbf{(0.440,0.660)}$

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