Question
4. The Old Towne Road Group sent its' top specialist, Tegan (aka Stat Buddees) to get information on why the Street Farmacyst plastic bottles did not explode under pressure. They selected 36 Street Farmacyst bottles and got a mean of twenty-six with a population standard deviation of 1.5. a. What is the maximum error? ( (2pt.) b. Help her construct an 80% confidence interval for the mean number of plastic bottles that did not explode under pressure. (3pts)
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Answer to a math question 4. The Old Towne Road Group sent its' top specialist, Tegan (aka Stat Buddees) to get information on why the Street Farmacyst plastic bottles did not explode under pressure. They selected 36 Street Farmacyst bottles and got a mean of twenty-six with a population standard deviation of 1.5. a. What is the maximum error? ( (2pt.) b. Help her construct an 80% confidence interval for the mean number of plastic bottles that did not explode under pressure. (3pts)
Hermann
4.6120 Answers
a. Maximum error:
First, find the z-value for an 80% confidence interval:
z_{\alpha/2} = 1.2816
Then use the formula for the maximum error:
E = z_{\alpha/2} \frac{\sigma}{\sqrt{n}}
E = 1.2816 \times \frac{1.5}{\sqrt{36}}
E = 1.2816 \times 0.25
E=0.3204
b. 80% confidence interval:
The formula for the confidence interval is:
\text{CI} = \left( \bar{x} - E , \bar{x} + E \right)
Given:
\bar{x} = 26
E=0.3204
Substituting the values:
\text{CI}=\left(26-0.3204,26+0.3204\right)
\text{CI}=(25.6796,26.3204)
First, find the z-value for an 80% confidence interval:
Then use the formula for the maximum error:
b. 80% confidence interval:
The formula for the confidence interval is:
Given:
Substituting the values:
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