Question

There is concern about the speed of automobiles traveling over highway E311. For a random sample of seven automobiles radar indicated the following speeds, in kilometers per hour: 140, 154, 99, 138, 137, 142, and 130.
a. Assuming a normal population distribution, estimate with 95% confidence the mean speed of all automobiles.

How to find s ?

Answer 1

n=7

c=95%

Calculate sample mean and sample standard deviation for the given data as follows

x	(x-x̅ )	(x - x̅)²
140	5.714286	32.65306
154	19.71429	388.6531
99	-35.2857	1245.082
138	3.714286	13.79592
137	2.714286	7.367347
142	7.714286	59.5102
130	-4.28571	18.36735
940	805.7143	649175.5
1880		650940.9

Mean = ∑x/n         =1880/7     =134.2857

Sample standard deviation = √(∑(x - x̅)²/n-1)     =√(50940.9/7-1)     =17.1533

thus we get sample mean and sample standard deviation for the given data as follows

= 134.2857

s= 17.1533

now formula for confidence interval is

where tc is the t critical value with c= 95% and df = n-1 = 7-1 = 6

find tc using t table, we get

tc = 2.447

118.42 < < 150.15

confidence interval is  (118.42 , 150.15)