Respuesta :
Answer:
a) [tex]56.4 \leq \mu \leq 60.8[/tex] with [tex] \bar X= 58.6[/tex]
[tex]Width= \frac{60.8-56.4}{2}=2.2[/tex]
Since this represent the second largest width interval needs to represent the c=0.95 or 95% confidence interval.
b) [tex]55.7 \leq \mu \leq 61.5[/tex] with [tex] \bar X= 58.6[/tex]
[tex]Width= \frac{61.5-55.7}{2}=2.9[/tex]
Since this represent the largest width interval needs to represent the c=0.99 or 99% confidence interval.
c) [tex]56.8 \leq \mu \leq 60.4[/tex] with [tex] \bar X= 58.6[/tex]
[tex]Width= \frac{60.4-56.8}{2}=1.8[/tex]
Since this represent the smallest width interval needs to represent the c=0.99 or 88% confidence interval.
d)[tex]56.7 \leq \mu \leq 60.5[/tex] with [tex] \bar X= 58.6[/tex]
[tex]Width= \frac{60.5-56.7}{2}=1.9[/tex]
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".
[tex]\bar X=58.6[/tex] represent the sample mean for the sample
[tex]\mu[/tex] 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) [tex]56.4 \leq \mu \leq 60.8[/tex] with [tex] \bar X= 58.6[/tex]
We can find the width of the interval like this:
[tex]Width= \frac{60.8-56.4}{2}=2.2[/tex]
Since this represent the second largest width interval needs to represent the c=0.95 or 95% confidence interval.
b) [tex]55.7 \leq \mu \leq 61.5[/tex] with [tex] \bar X= 58.6[/tex]
We can find the width of the interval like this:
[tex]Width= \frac{61.5-55.7}{2}=2.9[/tex]
Since this represent the largest width interval needs to represent the c=0.99 or 99% confidence interval.
c) [tex]56.8 \leq \mu \leq 60.4[/tex] with [tex] \bar X= 58.6[/tex]
We can find the width of the interval like this:
[tex]Width= \frac{60.4-56.8}{2}=1.8[/tex]
Since this represent the smallest width interval needs to represent the c=0.99 or 88% confidence interval.
d)[tex]56.7 \leq \mu \leq 60.5[/tex] with [tex] \bar X= 58.6[/tex]
We can find the width of the interval like this:
[tex]Width= \frac{60.5-56.7}{2}=1.9[/tex]
Since this represent the third largest width interval needs to represent the c=0.90 or 90% confidence interval.
Based on the level of confidence, the corresponding normal confidence intervals will be:
- c = 0.88 = Confidence interval is 56.80 - 60.4.
- c = 0.9 = Confidence interval is 56.7 - 60.5.
- c = 0.95 = Confidence interval is 56.4 - 60 8.
- c = 0.99 = Confidence interval is 55.7 to 61.5.
What are the corresponding normal confidence intervals?
The rule here is that the higher the level of confidence, the higher the corresponding normal interval.
The lowest level of confidence will therefore correspond to the lowest normal interval.
For this reason, the level of confidence of 0.88 will correspond to the lowest confidence interval of 56.80 - 60.4.
This continues till the highest level of confidence = 0.99 corresponding to the highest confidence interval = 55.7 - 61.5.
Find out more on confidence intervals at https://brainly.com/question/13160716.
