Question

Data

T2005    AZ100

3.06        2.91

3.04        3.31

3.13        2.82

3.01        3.01

2.95        2.94

3.02        3.17

3.02        3.25

3.12        3.39

3.00        3.22

3.04        2.97

3.03        2.93

3.05        2.97

3.01        3.05

2.73        2.95

3.12        2.92

3.04        2.71

3.10        2.77

3.02        2.73

2.92        3.18

3.01        2.95

3.15        2.86

2.69        3.16

3.04        3.06

3.01        3.25

2.95        2.82

3.14        3.22

3.31        2.93

3.01        3.24

2.93        2.77

3.00        2.94

3.04        3.31

To determine the precision of the two drills, you examine the variance in the sample data for the two samples. Conduct a test of the hypothesis that the T2005 and the AZ100 are equally precise (that they have equal variances). What is the value of your test statistic?

3.022

2.854

0.350

3.023

Construct a 99% confidence interval around the mean difference between the T2005 and AZ100 drills. What is the lower limit of the confidence interval assuming an unknown population standard deviations?

Unknown

-0.080

-0.107

-.067

Conduct a hypothesis test to determine if the AZ100 drill holes are statistically significantly different from the hypothesized value of 3 centimeters. Use an alpha of .05, and assume the population standard deviation is unknown. What is the value of your test statistic?

1.100

0.020

0.670

0.034

What is the population standard deviation for 3 centimeter holes drilled by the AZ100 drill?

0.002

0.113

Unknown

0.190

Answer 1

1)

Null and alternative hypothesis:
Hₒ : σ₁² = σ₂²
H₁ : σ₁² ≠ σ₂²

   Sample :     AZ100
Sample Standard deviation,    s₁ =    0.112626512
Sample size,    n₁ =    31

   Sample : T2005
Sample Standard deviation,    s₂ =    0.190266367
Sample size,    n₂ =    31

Test statistic:  
F = s₁² / s₂² = 0.1903² / 0.11263² =    2.854

================

2)

t-critical value =    t α/2 =    2.682   (excel formula =t.inv(α/2,df)      
                  
                  
                  
std error , SE =    √(s1²/n1+s2²/n2) =    0.040          
margin of error, E = t*SE =    2.682   *   0.040   =   0.106513
                  
difference of means = x̅1-x̅2 =    3.0223   -   3.023   =   -0.0006
confidence interval is                   
Interval Lower Limit = (x̅1-x̅2) - E =    -0.0006   -   0.107   =   -0.107
=====================

Ho :   µ =   3  
Ha :   µ ╪   3   (Two tail test)
          
Level of Significance ,    α =    0.050  
sample std dev ,    s =    0.1903  
Sample Size ,   n =    31  
Sample Mean,    x̅ =   3.0229  
          
degree of freedom=   DF=n-1=   30  
          
Standard Error , SE = s/√n =   0.1903/√31=   0.0342  
t-test statistic= (x̅ - µ )/SE =    (3.0229-3)/0.0342=   0.670  
======================

population standard deviation for 3 centimeter holes drilled by the AZ100 drill = unknown