When 328 college students are randomly selected and suveyed

When 328 college students are randomly selected and suveyed, it is found that 122 own a car.

a) Find the best point estimate of the population proportion of all college students who own a car. round to 3 decimal places.

b)For 99% confidence level,find the margin of error E and construct a confidence interval for the true population proportion of all college students who own a car. Round to 3 decimal places.

c)Write a brief statement that correctly interprets the confidence interval obtained in part \"b\".

d) What does the confidence interval suggest about the common belief that 50% of all college students own a car?

Solution

a)
Sample proportion = x/n =0.372
b)
Margin of Error = Z a/2 Sqrt(p*(1-p)/n))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=122
Sample Size(n)=328
Sample proportion =0.372
Margin of Error = Z a/2 * ( Sqrt ( (0.372*0.628) /328) )
= 2.58* Sqrt(0.0007)
=0.0689

CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=122
Sample Size(n)=328
Sample proportion = x/n =0.372
Confidence Interval = [ 0.372 ±Z a/2 ( Sqrt ( 0.372*0.628) /328)]
= [ 0.372 - 2.58* Sqrt(0.0007) , 0.372 + 2.58* Sqrt(0.0007) ]
= [ 0.3031,0.4409]
c)
We are 99% confident that the mean value lie sin the interval stated in part b
d)
It is n\'t true, 50% of all college students own a car is out of bound