Question

Asked Apr 24, 2019

242 views

Step 1

**Finding the 95% confidence interval for the proportion of women with cosmetic dermatitis from using eye shadow who have a nickel allergy:**

The sample of 131 women with cosmetic dermatitis from using eye shadow. Among 12 are diagnosed with a nickel allergy. That is, the sample size *n = *131 and *x* *= *12. Therefore, the sample proportion *p*-hat is 12 / 131 = 0.0916. The 100(1 – α)% confidence interval of *p* is,

Step 2

The confidence interval is 95%.

Therefore, α = 0.05.

The test is two tailed and the z- value corresponding to significance level 0.05 is 1.96.

Therefore, the 95% confidence interval of population proportion is,

Step 3

**Interpretation:**

There is 95% confident that the true proportion value of women with cosmetic dermatitis f...

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