Question

Listed below are the speed ((mi/h) measured from the Southbound traffic on I-280. The speed limit is 65 mph.

62, 61, 61, 57, 61, 54, 59, 58, 59, 69, 60, and 67

1.Construct a 95% confidence interval.

2.What will happen to the width of the confidence interval if the confidence level is increased to 99%? Explain

3. What will happen to the accuracy of the estimate if the sample size is increase

Answer 1

1.

CI = mean + /- E

t value for 95% of confidence interval at 11 df is TINV(0.05,11) = 2.201

n = 12

sample mean = sum of all terms / no of terms = 728/ 12 = 60.667

sample sd = s

data	data-mean	(data - mean)2
62	1.3333	1.77768889
61	0.3333	0.11108889
61	0.3333	0.11108889
57	-3.6667	13.44468889
61	0.3333	0.11108889
54	-6.6667	44.44488889
59	-1.6667	2.77788889
58	-2.6667	7.11128889
59	-1.6667	2.77788889
69	8.3333	69.44388889
60	-0.6667	0.44448889
67	6.3333	40.11068889

CI = 60.667 +/- 2.589

CI = (58.078 ,    63.256)

2. If the CI is increased to 99%, t value will be 3.106, E = 3.654

CI = (57.013 , 64.321)

Width of confidence interval increases as Confidence interval is increased. This is beacuse Margin of error increases.

3. If the sample size is increased, the standard error will reduce. As a result the width of confidence interval decreases. This will increase the estimate of accuracy.