A summer intern at the Lego factory in Billund, Denmark, samples 42 yellow brick

Question

A summer intern at the Lego factory in Billund, Denmark, samples 42 yellow bricks and 26 red bricks and measures their weight. She nds sample means of 4.1 grams (yellow bricks) and 4.2 grams (red bricks), and sample standard deviations of 0.15 (yellow) and 0.23 (red), respectively.

(a) Compute the 95% condence interval for the mean weight of red bricks.

(b) Compute the 95% condence interval for the dierence between the mean weights (i.e., red minus yellow).

(c) Compute the 95% condence interval for the variance of the weight for the yellow bricks.

For each question above, make sure you state clearly which distribution you are using, what assumptions that entails, and whether there could be alternate choices.

Explanation / Answer

n2 =26X2 =4.2s2 =0.23

95%confidence interval for the mean weight of red bricks

              X2 ± t0.05   * s­2/n2

             4.2 ± 2.06 *0.23/26

               [4.1071 , 4.2929]

Given n1 =42X1 = 4.1s1= 0.15

            n2 =26    X2 = 4.2    s2= 0.23

S.E(X1 -   X2) = (s12/n1)+ (s22/n2) = ((0.15)2/42)+ ((0.23)2/26)

                              = 0.0026 = 0.0507

95% confidence interval is

X1 -   X2 ± 1.96 * S.E(X1 -   X2)

4.1 – 4.2 ± 1.96 * 0.0507

0.1 ± 1.96 * 0.1245

[0.0006 , 0.1994]

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