Mathematics, 27.12.2019 01:31 Jmajano99

For each level of confidence c below, determine the corresponding normal confidence interval. assume each confidence interval is constructed for the same sample statistics.

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Answer from: kyleee1991

a) $56.4 \leq \mu \leq 60.8$ with $\bar X= 58.6$

$Width= \frac{60.8-56.4}{2}=2.2$

Since this represent the second largest width interval needs to represent the c=0.95 or 95% confidence interval.

b) $55.7 \leq \mu \leq 61.5$ with $\bar X= 58.6$

$Width= \frac{61.5-55.7}{2}=2.9$

Since this represent the largest width interval needs to represent the c=0.99 or 99% confidence interval.

c) $56.8 \leq \mu \leq 60.4$ with $\bar X= 58.6$

$Width= \frac{60.4-56.8}{2}=1.8$

Since this represent the smallest width interval needs to represent the c=0.99 or 88% confidence interval.

d) $56.7 \leq \mu \leq 60.5$ with $\bar X= 58.6$

$Width= \frac{60.5-56.7}{2}=1.9$

Since this represent the third largest width interval needs to represent the c=0.90 or 90% confidence interval.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=58.6$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence levels provided are :

c=0.88, c=0.90, c=0.95, c =0.99

And we need to associate each confidence level with the interval

We have the following intervals:

a) $56.4 \leq \mu \leq 60.8$ with $\bar X= 58.6$

We can find the width of the interval like this:

$Width= \frac{60.8-56.4}{2}=2.2$

Since this represent the second largest width interval needs to represent the c=0.95 or 95% confidence interval.

b) $55.7 \leq \mu \leq 61.5$ with $\bar X= 58.6$

We can find the width of the interval like this:

$Width= \frac{61.5-55.7}{2}=2.9$

Since this represent the largest width interval needs to represent the c=0.99 or 99% confidence interval.

c) $56.8 \leq \mu \leq 60.4$ with $\bar X= 58.6$

We can find the width of the interval like this:

$Width= \frac{60.4-56.8}{2}=1.8$

Since this represent the smallest width interval needs to represent the c=0.99 or 88% confidence interval.

d) $56.7 \leq \mu \leq 60.5$ with $\bar X= 58.6$

We can find the width of the interval like this:

$Width= \frac{60.5-56.7}{2}=1.9$

Since this represent the third largest width interval needs to represent the c=0.90 or 90% confidence interval.

Answer from: Quest

If i'm correct the answer is $15.97

Answer from: Quest

a is the correct

And do not get it wrong . this is a quiz and im struggling ! ☹️

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