Solved Problems

A sample of 50 soil specimens has a mean shear strength of 2500 psf with a standard deviation of 300 psf. Construct a 95% confidence interval for the true mean shear strength.

A civil engineer measures the setting time of a newly developed quick-set concrete mix. A random sample of $n = 12$ batches yields a sample mean setting time of $\bar{x} = 45$ minutes and a sample standard deviation of $s = 4.5$ minutes. Assuming the setting times are normally distributed, construct a 99% confidence interval for the true mean setting time.

Two suppliers provide steel rebars. A sample of 40 rebars from Supplier A has a mean yield strength of 420 MPa with a standard deviation of 15 MPa. A sample of 35 rebars from Supplier B has a mean yield strength of 410 MPa with a standard deviation of 18 MPa. Construct a 90% confidence interval for the difference in true mean yield strengths ($\mu_A - \mu_B$).

A structural assessment team inspects 200 randomly selected bridges in a state and finds that 35 of them are structurally deficient. Determine a 95% confidence interval for the true proportion of structurally deficient bridges in the state.