Pigmented makeup products like mascara and eye shadow may contain metal (e.g., nickel) allergens. Is a nickel allergy more likely to occur in women who report cosmetic dermatitis from using eye shådów of masci women with cosmetic dermatitis from using eye shadow, 11 were diagnosed with a nickel allergy. In a sample of 258 women with cosmetic dermatitis from using mascara, 27 were diagnosed with a nickel allergy. Use this information to com parts a through c below. mple of 130 a. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using eye shadow who have a nickel allergy. The 95% confidence interval for eye shadow is (Round to three decimal places as needed.) Interpret the result. Choose the correct answer below. O A. With 95% confidence, the sample proportion of women with cosmetic dermatitis from using eye shadow that have a nickel allergy is in this interval. O B. With 95% confidence, the population proportion of women with cosmetic dermatitis from using eye shadow that have a nickel allergy is in this interval. O c. With 95% confidence, any sample proportion of women with cosmetic dermatitis from using eye shadow that have a nickel allergy will be in this interval. O D. With 95% confidence, the population proportion women that have a nickel allergy is in this interval. b. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using mascara who have a nickel allergy The 95% confidence interval for mascara is ( A D (Round to three decimal places as needed.)