Question

1. A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected, and the diameter is measured. The resulting data (in millimeters) are as follows: 11.44 11.39 11.35 11.38 11.45 11.4311.4211.44 11.34 11.39 11.46 11.36 11.44 11.49 11.41 a) Use a Normal Probability Plot to check the assumption of normality for rod diameter. b) Is it believable the mean rod diameter is less than 1 1.50 mm? Construct the appropriate 99% confidence interval

Answer 1

a)

Rank	Proportion	Z Value	Data:
1	0.063	-1.534	11.34
2	0.125	-1.150	11.35
3	0.188	-0.887	11.36
4	0.250	-0.674	11.38
5	0.313	-0.489	11.39
6	0.375	-0.319	11.39
7	0.438	-0.157	11.41
8	0.500	0.000	11.42
9	0.563	0.157	11.43
10	0.625	0.319	11.44
11	0.688	0.489	11.44
12	0.750	0.674	11.44
13	0.813	0.887	11.45
14	0.875	1.150	11.46
15	0.938	1.534	11.49

the S shape of the graph in the normal probability plot indicates that distribution is approximately normal.

b)

mean=   11.41    [Excel function used -> AVERAGE]
sd=   0.05    [Excel function used -> STDEV]  
n=   15.00    [Excel function used -> COUNT]
alpha=   1%
critical value, t(a/2,n-1) = t(0.01/2,15-1) = 2.977

CI = mean +- t(a/2,n-1)*(sd/sqrt(n))      
lower = 11.4129 - 2.977*(0.045/sqrt(15)) = 11.38
upper = 11.4129 + 2.977*(0.045/sqrt(15)) = 11.45

i am 99% confident that estimated population mean rod diameter lie in this interval (11.38, 11.45). Since this interval has all values less than 11.5, i can say that, it is believable that mean rod diameter is less than 11.5.