Many restaurants are now offering “healthy” items on their menus. Research suggests that these items may increase sales and profits because more Americans claim to be eating healthier foods. In a...

Many restaurants are now offering “healthy” items on their menus. Research suggests that these items may increase sales and profits because more Americans claim to be eating healthier foods. In a recent survey by the NPD Group, only 25% of adults say they eat healthy foods when they dine at restaurants.28 A random sample of 260 adults was asked if they eat healthy foods when they dine out. Seventy adults indicated they eat healthy foods at restaurants.

 a. Find a 95% confidence interval for the true proportion of adults who eat healthy foods when they dine out.

 b. Is there any evidence to suggest that the claim of p 5 0.25 is wrong? Justify your answer.

A new standard for 30-, 40-, and 50-gallon residential gas water heaters includes a flame arrester. This device helps to prevent flashback fires from flammable liquid vapor nearby. The Consumer Product Safety Commission would like to estimate the proportion of homes affected by this safety standard.

 a. In a random sample of 575 homes, 235 had gas water heaters. Find a 90% confidence interval for the true proportion of homes with gas water heaters. Write a Solution Trail for this problem.

b. Prior research suggests that the proportion of homes with gas water heaters is approximately 0.40. How large a sample is necessary for the bound on the error of estimation to be 0.03 for a 95% confidence interval?