Let $\overline{XY}$ be a tangent to a circle, and let $\overline{XBA}$ be a secant of the circle, as shown below. If $AX = 15$ a
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Answer:
0.0406, 0.8284,0.7887
Step-by-step explanation:
Given that Mattel Corporation produces a remote-controlled car that requires three AA batteries
X is N(34, 5.5)
Hence sample size of 25 would follow a t distribution with df = 24
This is because sample size <30
t distribution with df 24 would be bell shaped symmetrical about the mean and unimodal.
Std error of sample mean = std dev /sqrt n=
Prob (X>36) =
i.e nearly 4.1% of the sample would have a mean useful life of more than 36 hours
X>33.5 implies
=0.82837
=0.8284 proportion will have a mean useful life greater than 33.5 hours
Proportion between 33.5 and 36 hours
=
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.