Many restaurants are now offering \"healthy\" items on their menus. Research sug

Question

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 = 0.25 is wrong? Justify your answer.

Explanation / Answer

p=70/260=0.269 ; n=269

std error =(p(1-p)/n)1/2 =0.0275

for 95% confidence interval; z=1.96

hence confidence interval =estimated proportion -/+ z*std error =0.215 ; 0.323

b)as above confidence interval contains 0.25 as a probable value; we do not have evidence to suggest that the claim of p=0.25 is wrong.

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