An automobile’s color is one of the factors that influences a consumer’s demand for it. Suppose a car manufacturer in your country is planning to launch a new model and is deciding on the colors that can be offered. The manufacturer is wondering whether silver, at 28.3%, is still leading choice for prospective consumers in the country’s population. He selects a random sample of 450 consumers’ opinions and found that 117 consumers selected the color silver as their preferred choice.

a. Calculate the best point estimate and compare it with the population value.

b. Calculate a 95% confidence interval for the true proportion of consumers who favor the silver color.

Based on your findings, determine whether the given parameter value is a reliable one.

c. If the manufacturer wants to estimate the population proportion of consumers who prefer the color silver within a margin of error of {0.03 with the same level of confidence as in part

b, what would be the additional samples required by the manufacturer?