Arandom sample of size n1 = 25, taken from a normal population with a standard deviation σ1 = 5, has a mean ¯x1 = 80. a second random sample of size n2 = 36, taken from a different normal population with a standard deviation σ2 = 3, has a mean ¯x2 = 75. find a 94% confidence interval for μ1 − μ2.

4.08 < μ1 − μ2 < 5.94

Step-by-step explanation:

The confidence level interval for μ is given by;

    = ⁻x ± z*

where  n = Sample size

            σ = Standard deviation

             ⁻x =  Mean

For  a Confidence level = 94%, the critical value is z = 1.88

Considering the first random sample:

              n1 = 25

              σ1 = 5

                ⁻x1 = 80

The confidence level interval for μ1 is given by;

   μ1 = ± 1.88 ×

   μ1 = 80  ± (1.88 ×1) = 80  ± 1.88

    μ1 = 78.12 < μ1 < 81.88

For the second random sample

              n2 = 36

              σ2 = 3

                ⁻x2 = 75

The confidence level interval for μ2 is given by;

  μ2 = ± 1.88 ×

   μ2 = 75  ± (1.88 × 0.5) = 75 ± 0.94

   μ2 = 74.04 < μ2 < 75.94

For the interval μ1 − μ2,

The confidence level is 78.12 - 74.04 < μ1 − μ2 < 81.88 - 75.94

4.08 < μ1 − μ2 < 5.94

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