Question

Confidence Interval (Breaking Distance of Cars) 

Please collect the data and draw your assumptions.  

1. Using the raw data  select the sample that represents the breaking distance of specific cars. Let X represent the number of cars whose breaking distance was less than 130 feet. Use this information to find the confidence interval for the percentage of cars whose breaking distance is less than 130 feet.
2. n = ____________  
3. x = ____________  

State your assumption:  

2. In words, define the random variable (sample proportion).  
3. State the estimated distribution to use.  
4. Use an appropriate graph to illustrate the data 

 

Using what you have learned in the class to identify and solve the problem.  

Find the Error and Confidence Interval

5. How much area is in both tails (combined)? α = _____  
6. How much area is in each tail? α/2 = _____
7. What is z?2 =   
8. Construct the interval: 
9. Error: _____ 
10. Confidence Interval: _____  
11. Fill in the blanks on the graph with the area in each section. Then, fill in the number line with the upper and lower limits of the confidence interval and the sample proportion.  

 

10.  Fill in the table: 

Confidence Level	Error	Confidence Interval
50%
80%
95%
99%

DATA

(133,136,126,137,138,132,135,136,136,128,140,140,135,137,139,134,145,143,131,140,143)

Answer 1

n = 21

x = 2

The random variable (sample proportion) is the number of cars whose braking distance was less than 130 feet.

The distribution to use is the One-proportion z-test.

Confidence level	Error	Confidence Interval
50%	0.0432	(0.052, 0.1384)
80%	0.0821	(0.0131, 0.1773)
95%	0.1255	(-0.0303, 0.2208)
99%	0.165	(-0.0698, 0.2602)

As the confidence level increases, the error rate increases and the results become less significant.

11. As the confidence level increases, the error rate increases and the width of the confidence interval increases.