A civil engineer is analyzing the compressive strength of concrete. Compressive

Question

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed. A random sample of 12 specimens has a compressive strength of x bar = 3250 psi and s^2 = 1000(psi)^2. (a) Construct a 95% two-sided confidence interval on the mean compressive strength. (b) Construct a 99% two-sided confidence interval on the mean compressive strength. Compare the width of this confidence interval with the width of the one found in part (a). (c) Find a 99% one-sided lower confidence bound on the mean compressive strength. (d) Find a 99% one-sided upper confidence bound on the mean compressive strength.

Explanation / Answer

a) We know the values and given that

= 0.05, Z/2 = 1.96, ¯x = 3250, 2 = 1000, n = 12

now the 95% two-sided CI on µ is

so x¯ Z/2 / n µ x¯ + Z/2 /n

3250 (1.96) · 1000/ 12 µ 3250 + (1.96) · 1000 / 12

3232.11 µ 3267.89.

b ans) For = 0.01, z/2 = 2.58.

So the 95% two-sided CI on µ is

x¯ Z/2 n µ x¯ + Z/2 n

3250 (2.58) · sqrt1000 12 µ 3250 + (2.58) · 1000 12

3226.4 µ 3273.6.

The 99% CI is wider than the 95% CI

c ans ) well we have already found two intervals above

so one sided lower confidence bound is 3226.4

d ans)

well we have already found two intervals above

so one sided upper r confidence bound is 3273.6

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