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Suppose data collected by observers at randomly selected intersections across the country revealed that in a sample of 400 drivers, 380 were using their cell phone. 
a. Give a point estimate of it, the true driver cell phone use rate (that is, the true proportion-or-population porportion- of drivers who are using their cell phone while driving). 
b. Compute a 95% confidence interval for it. 
c. Give a practical interpretation of the interval, part b.
 

The estimate of the population proportion is found by dividing x (people using cell phone while driving) by n (The sample size of drivers selected). point estimate is 380/400 = 0.95

The standard normal distribution is applied as it is assumed that the responses are normally distributed.  

Confidence interval = p_hatch +/- Margin of error

p_hatch = 0.95

The margin of error = z_score * sqrt(p_hatch * (1-p_hatch)/n)

ME = 1.96 (This changes depending on the confidence interval level that is being constructed) * SE

SE = sqrt(p_hatch * (1-p_hatch)/n) ;= sqrt(0.95 * (1-0.95)/400) = 0.0109

Confidence interval = 0.95 +/- 0.0109, hence the confidence interval is (0.9391, 0.9609).

One is 95% confident that the true population proportion is within the interval constructed, that is between (0.9391,0.9609)

 

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