Question

Use the data to calculate the sample variance, s2. (Round your answer to five decimal places.) n = 10: 19.1, 9.7, 11.9, 8.5, 10.8, 9.0, 7.3, 12.6, 14.8, 12.2

Construct a 95% confidence interval for the population variance, σ². (Round your answers to two decimal places.)

_____ to _____

Test H₀: σ² = 9 versus H_a: σ² > 9 using α = 0.05.

State the test statistic. (Round your answer to two decimal places.)

χ² =  

State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to four decimal places.)

χ2	>
χ2	<

Answer 1

variance of sample =11.8943

Sample Size,   n=   10
Sample Standard Deviation,   s=   3.4488
Confidence Level,   CL=   0.95
      
      
Degrees of Freedom,   DF=n-1 =    9
alpha,   α=1-CL=   0.05
alpha/2 ,   α/2=   0.025
Lower Chi-Square Value=   χ²1-α/2 =   2.7004
Upper Chi-Square Value=   χ²α/2 =   19.0228
      
95%   confidence interval for variance is  
lower bound= (n-1)s²/χ²α/2 =   9*3.4488² / 19.0228=   5.627
      
upper bound= (n-1)s²/χ²1-α/2 =   9*3.4488² / 2.7004=   39.642

/.....................

Ho :   σ² =   9
Ha :   σ² >   9
      
Level of Significance ,    α =    0.05
sample Variance,   s² =    11.8943
Sample Size ,   n =    10
      
Chi-Square Statistic   X² = (n-1)s²/σ² =    11.89
      
degree of freedom,   DF=n-1 =    9
      
one tail test       
Upper Critical Value   =   16.9190

Do not reject the null hypothesis

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