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?
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.
Thanks in advance!
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