The accompanying data is on cube compressive strength (MPa) of concrete specimens. 112.1 97.0 92.8 86.0 102.0
99.2 95.8 103.5 89.0 86.9
(a) Is it plausible that the compressive strength for this type of concrete is normally distributed?
1. The normal probability plot is acceptably linear, suggesting that a normal population distribution is not plausible.
2. The normal probability plot is not acceptably linear, suggesting that a normal population distribution is plausible.
3. The normal probability plot is not acceptably linear, suggesting that a normal population distribution is not plausible.
4. The normal probability plot is acceptably linear, suggesting that a normal population distribution is plausible.
(b) Suppose the concrete will be used for a particular application unless there is strong evidence that true average strength is less than 100 MPa. Should the concrete be used? Carry out a test of appropriate hypotheses.
State the appropriate hypotheses.
1. H0: μ < 100
Ha: μ = 100
2. H0: μ = 100
Ha: μ ≠ 100
3. H0: μ > 100
Ha: μ = 100
4. H0: μ = 100
Ha: μ > 100
5. H0: μ = 100
Ha: μ < 100
(c) Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
t =
P-value =
(d) What can you conclude?
1. There is strong evidence that the true average strength is less than 100 MPa. The concrete should not be used.
2. There is not strong evidence that the true average strength is less than 100 MPa. The concrete should be used.