Question

Experimental data are obtained with a supply of steel reinforcing bars (36 samples, mean yield strength = 20 kips) from the original supplier of bars and standard deviation is known to be 2.4 kips. A Civil Engineer finds an alternative supplier of steel reinforcing bars. The new reinforcing bars have a known yield strength of 23 kips on average and standard deviation = 2.4 kips. Can the engineer suggest with 95% confidence that the reinforcing bars from the original supplier have a lower yield strength than those from the alternative supplier (23 kips)?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 23
Alternative Hypothesis, Ha: μ < 23

Rejection Region
This is left tailed test, for α = 0.05
Critical value of z is -1.645.
Hence reject H0 if z < -1.645

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (20 - 23)/(2.4/sqrt(36))
z = -7.50

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.

yes, engineer suggest with 95% confidence that the reinforcing bars from the original supplier have a lower yield strength than those from the alternative supplier