Question

A marketing research firm wants to estimate the share that foreign companies have in the American market for certain products. A random sample of 100 consumers is obtained, and it is found that 34 people in the sample are users of foreign made products the rest are users of domestic products. Give a 95% confidence interval estimate for the share of foreign products in this market.

Answer 1

To estimate the share of foreign products in the American market, a 95% confidence interval for the proportion of 0.34, based on a sample of 100 consumers with 34 users of foreign products, is calculated to be approximately (0.25, 0.43).

Step-by-step explanation:

To estimate the share of foreign products in the American market for certain products, we can calculate a 95% confidence interval around the sample proportion. In the given scenario, a random sample of 100 consumers revealed 34 users of foreign made products, yielding a sample proportion (p') of 0.34 for foreign product usage.

Using the standard formula for a confidence interval, where 'p' is the sample proportion, 'n' is the sample size, and 'Z' is the Z-score for the desired confidence level (1.96 for 95% confidence), the confidence interval (CI) formula looks like this:

CI = p ± Z * sqrt(p(1 - p) / n)

Plugging our numbers:

• p = 0.34
• n = 100
• Z = 1.96

The confidence interval calculation is:

CI = 0.34 ± 1.96 * sqrt(0.34 * (1 - 0.34) / 100)

Now, simplifying:

CI = 0.34 ± 1.96 * sqrt(0.34 * 0.66 / 100)

CI = 0.34 ± 1.96 * sqrt(0.2244 / 100)

CI = 0.34 ± 1.96 * sqrt(0.002244)

CI = 0.34 ± 1.96 * 0.04738

CI = 0.34 ± 0.09286

CI = 0.34 ± 0.09

Thus, the 95% confidence interval estimate for the share of foreign products is approximately (0.25, 0.43).