To complete one round of a jogging track, Samantha took 1.52 minutes. Which expression below represents the time taken by Samant
2 answers:
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Answer:
a)
So then we can conclude that the true proportion of women with cosmetic dermatitis from using eye shadow at 95% of confidence is between (0.0422 and 0.1410)
b)
So then we can conclude that the true proportion of women with cosmetic dermatitis from using mascara at 95% of confidence is between (0.0628 and 0.1372)
c) For this case we see that both confidence intervals contains the value of 0.12 so then we can't conclude that only one group is referenced at the significance level of 0.05 used.
Step-by-step explanation:
Part a
The estimated proportion of women with cosmetic dermatitis from using eye shadow is given by:
The confidence interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
The confidence interval for the proportion is given by the following formula:
Replacing we got:
So then we can conclude that the true proportion of women with cosmetic dermatitis from using eye shadow at 95% of confidence is between (0.0422 and 0.1410)
Part b: A 95% confidence interval for the women with cosmetic dermatitis from using mascara
So then we can conclude that the true proportion of women with cosmetic dermatitis from using mascara at 95% of confidence is between (0.0628 and 0.1372)
Part c: 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.
For this case we see that both confidence intervals contains the value of 0.12 so then we can't conclude that only one group is referenced at the significance level of 0.05 used.