In a sample of 131 women with cosmetic dermatitis from using eye shadow, 12 were diagnosedwith a nickel allergy. In a sample of 250 women with cosmetic dermatitis from using mascara, 25were diagnosed with a nickel allergyCompute a 95% confidence interval for the proportion of women with cosmetic dermatitis fromusing eye shadow who have a nickel allergy. Interpret the result.Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis fromusing mascara who have a nickel allergy. Interpret the result.Suppose you are informed that the true proportion with a nickel allergy for one of the two groups(eye shadow or mascara) is.12. Can you determine which group is referenced? Explain.6.a)b)c)

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Asked Apr 24, 2019
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In a sample of 131 women with cosmetic dermatitis from using eye shadow, 12 were diagnosed
with a nickel allergy. In a sample of 250 women with cosmetic dermatitis from using mascara, 25
were diagnosed with a nickel allergy
Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from
using eye shadow who have a nickel allergy. Interpret the result.
Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from
using mascara who have a nickel allergy. Interpret the result.
Suppose you are informed that the true proportion with a nickel allergy for one of the two groups
(eye shadow or mascara) is.12. Can you determine which group is referenced? Explain.
6.
a)
b)
c)
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In a sample of 131 women with cosmetic dermatitis from using eye shadow, 12 were diagnosed with a nickel allergy. In a sample of 250 women with cosmetic dermatitis from using mascara, 25 were diagnosed with a nickel allergy Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using eye shadow who have a nickel allergy. Interpret the result. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using mascara who have a nickel allergy. Interpret the result. Suppose you are informed that the true proportion with a nickel allergy for one of the two groups (eye shadow or mascara) is.12. Can you determine which group is referenced? Explain. 6. a) b) c)

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Expert Answer

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,

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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,

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Step 3

Interpretation:

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

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