Question

Cement is one of the ingredients of concrete. Concrete is produced in “ready-mixed concrete plants.” Few years ago, a new type of cement entered the market. We want to find out what portion of the ready-mixed concrete plants use this new cement. Assume that there are 5,000 plants in the US. We select 100 plants and ask their managers if they use the new cement. We find that 20 of them use the new cement. For a confidence level of 95%, find the confidence interval for the percentage of ready-mixed concrete plants in the US that use the new cement

Answer 1

We need to construct the 95% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X =	20
Sample Size N =	100

The sample proportion is computed as follows, based on the sample size N = 100 and the number of favorable cases X = 20 :

The critical value for α=0.05 is z_c = 1.96. The corresponding confidence interval is computed as shown below: