Question

Inferences for a Single Variance Use the information in Exercises 7 and 8 to test Ho : 02 = 0% versus the given alternate hypothesis. Construct a (1 - a) 100% confidence interval for o2 using the x statistic. 7. n = 25, T = 126.3, s2 = 21.4, H:> 15, a = .05.

A. What is Ha?

B. What is the value of T=?

A. What is the critical value?

B. What is the correct decision?

C. What is the 95% CI for sigma?

C. What is the 95% CI for sigma?

Answer 1

1)
Ha :   σ² >   15
      
Level of Significance ,    α =    0.05
sample Variance,   s² =    21.4
Sample Size ,   n =    25
      
Chi-Square Statistic   X² = (n-1)s²/σ² =    34.24

2)

a)

Ho :   σ =   2
Ha :   σ ╪   2
      
Level of Significance ,    α =    0.05
sample Std dev ,    s =    1.914854216
Sample Size ,   n =    4
      
Chi-Square Statistic,   X² = (n-1)s²/σ² =    2.750
      
degree of freedom,   DF=n-1 =    3
Two-Tail Test      
Lower Critical Value   =   0.2158
Upper Critical Value   =   9.3484

b)

p-Value   =   0.431797081
      
Do not reject the null hypothesis      

c)

Sample Size,   n=   4
Sample Standard Deviation,   s=   1.9149
Confidence Level,   CL=   0.95
      
      
Degrees of Freedom,   DF=n-1 =    3
alpha,   α=1-CL=   0.05
alpha/2 ,   α/2=   0.025
Lower Chi-Square Value=   χ²1-α/2 =   0.216
Upper Chi-Square Value=   χ²α/2 =   9.348
          

confidence interval for std dev is       
lower bound= √[(n-1)s²/χ²α/2] =   √(3*1.9149² / 9.3484)=   1.0847
      
      
upper bound= √[(n-1)s²/χ²1-α/2] =   √(3*1.9149² / 0.2158)=   7.1396
      

                          

Please let me know in case of any doubt.

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