Question

The National Safety Council released a report in 2010 stating 20.12% of all traffic crashes involve drivers using cell phones and texting. The council would like to determine if this percentage has increased over the past three years. A random sample of 343 traffic crashes occurring in 2013 was selected, and it was determined whether or not the driver was using a cell phone during the accident. Describe the sampling distribution of the sample proportion of traffic crashes involving a cell phone when samples of 343 traffic crashes are taken. Round any calculated values to four decimal places. shape: The sampling distribution of the sample proportion is Checks (round to 4 decimal places): np = and n(1 - p) = mean: = standard deviation: σ ˆ p = The sample resulted in 50 traffic crashes involving a cell phone. Would this provide any support for the inference the council is interested in? The sample proportion is (round to 4 decimal places). This sample support the inference the council is interested in because it is than the proportion reported in 2010.

Answer 1

np = 343 * 0.2012 = 69.0116

n(1 - p) = 343(1 - 0.2012) = 273.9884

Mean = p = 0.2012

Standard deviation ($\sigma_{\widehat p}$) = sqrt(p(1 - p)/n)

= sqrt(0.2012(1 - 0.2012)/343)

= 0.0216

The sample proportion($\widehat p$) = 50/343 = 0.1458

This sample support the inference the council is interested in because it is less than the proportion reported in 2010.