A website reported that 31% of drivers 18 and older admitted to texting while driving in 2009. In a random sample of 800 drivers 18 years and older drawn in 2010, 204 of the drivers said they texted while driving. Complete parts a through c below. a. Construct a 99% confidence interval to estimate the actual proportion of people who texted while driving in 2010. A 99% confidence interval to estimate the actual proportion has a lower limit of nothing and an upper limit of nothing.
Solution :
Given that,
n = 800
x = 204
Point estimate = sample proportion = = x / n = 204 / 800 = 0.255
1 - = 1 - 0.255 = 0.745
At 99% confidence level
= 1 - 99%
=1 - 0.99 =0.01
/2
= 0.005
Z/2
= Z0.005 = 2.576
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 2.576 (((0.255 * 0.745) / 800)
= 0.040
A 99% confidence interval for population proportion p is ,
± E
= 0.255 ± 0.040
= ( 0.215, 0.295 )
lower limit = 0.215
upper limit = 0.295
A website reported that 31% of drivers 18 and older admitted to texting while driving in...
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