Answer:
a)
CI = ( 1.2718, 8.0614 )
Since value 2 is contained within Confidence Interval, fail to Reject H₀
b)
CI = ( -2.2296, 3.0296 )
Since value 2 is contained within Confidence Interval, fail to Reject H₀
c)
CI = ( 0.2962, 4.4538 )
Since value 2 is contained within Confidence Interval, fail to Reject H₀
Step-by-step explanation:
Given that;
Variance σ² = 9
so standard deviation σ = √9 = 3
with 95% confidence interval in each case. thus, The Z value for 95% confidence is Z = 1.96
Null Hypotheses H₀ : μ = 2
Now
a) (8,1,5)
sample mean x" = (8+1+5) / 3 = 14/3 = 4.6666
n = 3
Confidence Interval CI = x" ± ( z × σ/√n )
CI = 4.6666 ± ( 1.96 × 3/√3 )
CI = 4.6666 ± 3.3948
so CI = ( 1.2718, 8.0614 )
Since value 2 is contained within Confidence Interval, fail to Reject H₀
b) (8,1,5,-4,-8)
sample mean X" = (8 +1 + 5 - 4 - 8) / 5 = 2 / 5 = 0.4
n = 5
Confidence Interval CI = x" ± ( z × σ/√n )
CI = 0.4 ± ( 1.96 × 3/√5 )
CI = 0.4 ± 2.6296
so CI = ( -2.2296, 3.0296 )
Since value 2 is contained within Confidence Interval, fail to Reject H₀
c) (8,1,5,-4,-8,4,8,5)
sample mean x" = (8 + 1 + 5 - 4 - 8 + 4 + 8 + 5) / 8 = 19 / 8 = 2.375
n = 8
Confidence Interval CI = x" ± ( z × σ/√n )
CI = 2.375 ± ( 1.96 × 3/√8 )
CI = 2.375 ± 2.0788
so CI = ( 0.2962, 4.4538 )
Since value 2 is contained within Confidence Interval, fail to Reject H₀
