Homework 6
1. The sodium content of thirty 300-gram boxes of organic corn flakes was determined. The data
(in mg.) are as follows:
a) Can you support a claim that mean sodium content of this brand of corn flakes differs from 130
mg? use =0.05. Find the P-value.
131.15
130.69
130.91
129.54
129.64
128.77
130.72
128.33
128.24
129.65
130.14
129.29
128.71
129
129.39
130.42
129.53
130.12
129.78
130.92
131.15
130.69
130.91
129.54
129.64
128.77
130.72
128.33
128.24
129.65
H0: µ=130
H1:µ≠130
Variance unknown n<40 so use t test.
Test of mu = 130.000 vs mu not = 130.000
Variable
t
N
30
Mean
129.753
StDev
0.929
SE Mean
0.170
T
-1.46
P
0.16
P value=0.16 >0.05, we cannot reject the null hypothesis and conclude that sodium content of
this brand of corn flakes does not differs from 130 mg
b) Check the sodium content is normally distributed.
Normal probability plot show the normal distribution.
c) Compute the power of the test if the true mean sodium content is 130.5 mg.
Sample size=30, sigma=s= 0.929, d=0.5
1-Sample t Test
Testing mean = null (versus not = null)
Calculating power for mean = null + 0.5
Alpha = 0.05 Sigma = 0.929
Size
Power
30 0.8130
d) What sample size would be required to detect a true mean sodium content of 130.1 mg. if we
waned the power of the test to be at least 0.75?
1-Sample t Test
Testing mean = null (versus not = null)
Calculating power for mean = null + 0.1
Alpha = 0.05 Sigma = 0.929
Sample
Target Actual
Size
Power
Power
601
0.7500 0.7501
e) From question in a), construct a two-sided confidence interval on the mean sodium content.
Variable
N
Mean
StDev
SE Mean
95.0 % CI
t
30
129.753
0.929
0.170
( 129.406, 130.100)
95% CI include 130, so it is support the null hypothesis.
Homework7
1. An article in solid state technology describes an experiment to determine the effect of the C2F6
flow rate on the uniformly of the etch on a silicon wafer used in integrated circuit
manufacturing. Data for two flow rate are as follows:
C2F6
flow
rate
observation
1
2
3
4
5
6
125
2.7
4.6
2.6
3.0
3.2
3.8
200
4.6
3.4
2.9
3.5
4.1
5.1
a) Does the C2F6 flow rate affect average etch uniformity? Use =0.05
H0: µ1=µ2
H1: µ1≠µ2
n1=n2<40, variance unknown
We need to test the equal variance between two samples.
The slopes of their normal plot are equal so we can assume equal variance.
Two sample T for s1 vs s2
s1
s2
N
6
6
Mean
3.317
3.933
StDev
0.760
0.821
SE Mean
0.31
0.34
95% CI for mu s1 - mu s2: ( -1.63, 0.40)
T-Test mu s1 = mu s2 (vs not =): T = -1.35
Both use Pooled StDev = 0.791
P = 0.21
DF = 10
P value =0.21<0.05, we cannot reject the null hypothesis that is the average etch uniformity
from two samples are equal. We conclude that the flow rate does not affect the average etch
uniformity.
b) What is the P-value for the test in a)
P value-0.21
c) Does the C2F6 flow rate affect the variability in etch uniformity? Use =0.05
Draws box plots to assist in the interpretation of the data from this etch uniformity.
The box plots show that the variability of the average uniformity of two samples are about the same
(the width of boxes are equal) so we can conclude that different flow rate does not affect the variability.
2. A computer scientist is investigating the usefulness of two different design languages in
improving programming task. Twelve expert programmers, familiar with both languages, are
asked to code a standard function in both language, and the time (in minutes) is recorded. The
data follow:
a) Is the assumption that the difference in coding time is normally distributed reasonable?
Plot the normal plot of difference.
b) Find P-value for the test in a)
Each programmer codes both languages so using pair t test to analyze.
H0:µD=0 (no different between two language)
H1: µD≠0
Paired T for L1 - L2
L1
L2
Difference
N
12
12
12
Mean
17.92
17.25
0.667
StDev
3.63
4.59
2.964
SE Mean
1.05
1.33
0.856
95% CI for mean difference: (-1.217, 2.550)
T-Test of mean difference = 0 (vs not = 0): T-Value = 0.78
P-Value = 0.452
P value =0.452>0.05, we cannot reject the null hypothesis that is the mean difference between
time for coding L1 and L2 =0. We can conclude that different language does not affect the
coding time.
c) Find a 95% confidence interval on the difference in mean coding times. Is there any indication
that one design language is preferable?
d) 95% CI for mean difference: (-1.217, 2.550)
95% CI include 0 => the mean different of coding time between two languages is equal
to 0. No indication to support the claim that one design language is preferable.