You know that y is a normally distributed variable with a variance of 9. You do not know its mean. You collect some data. For each sample below, form the 95% confidence interval and test the null hypothesis of the mean equaling 2. a. (8,1,5)
b. (8,1,5,-4,-8)
c. (8,1,5,-4,-8,4,8,5)

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

answer: a.   one is a factor of every whole number since every number is divisible by itself.

so the possibilities of the measurement of the side of the triangle are either it is longest side or not the longest side

when it is the longest side

s < 25 + 35s < 60

if it is not the longest side

35 < 25 + s10 < sso 10 < s < 60so the perimeter70 < p < 130