1. A random sample of size 150 taken from a population yields a proportion equal
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Question
1. A random sample of size 150 taken from a population yields a proportion equal to 0.35.
a. Determine if the sample size is large enough so that the sampling distribution may be approximated by a normal distribution.
b. Produce the margin of error associated with 90% confidence.
c. Would the margin of error increase or decrease if we increase our level of confidence to 99%?
d. Would the margin of error increase or decrease if we increased the sample size to 600 (with 90% confidence)?
e. Describe the relationship between the margin of error in part b and part d.
2. In a July 2001 research note, the US Department of Transportation reported the results of the National Occupant Protection Use Survey. One focus of the survey was to determine the level of cell phone use by drivers while they are in the act of driving a motor passenger vehicle. Data collected by observers at randomly selected intersections across the country revealed that in a sample of 1165 drivers, 35 were using their cell phone.
a. Give a point estimate of p, the true driver cell phone rate
b. Check and verify the conditions for a 98% confidence interval.
c. Compute a 98% confidence interval for the proportion of drivers that are using their cell phones. Show the set-up for the interval.
d. Interpret the interval that you found in part c.
3. Suppose the federal government needs to estimate the proportion of students receiving federal loans that default on those loans. A previous similar study was found when doing research. The previous study estimated the proportion of students receiving federal loans that default on those loans to be 20%. Obtain a sample size that will ensure a margin of error of at most 0.04 for a 95% confidence interval.
4. How would your solution in problem 3 change if no prior knowledge of the proportion of students receiving federal loans was indicated?
Explanation / Answer
Ans:
1)
a)As,n=150>=30,so we can use normal approximation.
b)Margin of error=1.645*sqrt(0.35*(1-0.35)/150)=0.0641
c)Margin of error will increase,if confidence level is increased to 99%(as z value will increase to 2.58)
d)if sample size is increased to 600,margin of error will decrease.
e)margin of error increases,as we increase confidence level and margin of error decreases as we increase the sample size.
2)
a)point estimate of p=35/1165=0.03
b)z value for 98% CI is 2.33
c)98% CI of p
=0.03+/-2.33*sqrt(0.03*(1-0.03)/1165)
=0.03+/-0.012
=(0.018, 0.042)
3)
n=1.962*0.2*(1-0.2)/0.042
n=384
4)
n=1.962*0.5*(1-0.5)/0.042
n=600
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