Answer
384.3k+ views
Hint: We first express the concept of Confidence levels. We take an arbitrary example to understand the concept better.
Complete step by step solution:
Confidence levels are expressed as a percentage (for example, a 95% confidence level). It means that should you repeat an experiment or survey over and over again, 95 percent of the time your results will match the results you get from a population (in other words, your statistics would be sound). Confidence intervals are your results and they are usually numbers.
We constructed a 95% confidence interval for an experiment that found the sample mean temperature for a certain city in August was $\overline{x}=100$, with a population standard deviation of $\sigma =17.50$. There were 40 samples in this experiment.
The $\alpha $-level is $\dfrac{1-.95}{2}=.025$.
The formula is $\overline{x}\pm \left( z\times \dfrac{\sigma }{\sqrt{n}} \right)$. Here n is the number of samples. z is from the standard distribution tables (in the reference), and is $1.96$for a CI of 95%.
So, $\overline{x}\pm \left( z\times \dfrac{\sigma }{\sqrt{n}} \right)=100\pm \left( 1.96\times \dfrac{17.5}{\sqrt{40}} \right)=100\pm 5.42=\left[ 94.58,105.42 \right]$.
Note:
For example, if we survey a group of pet owners to see how many cans of dog food, they purchase a year. We test our statistics at the 99 percent confidence level and get a confidence interval of (200, 300). That means you think they buy between 200 and 300 cans a year. We are super confident (99% is a very high level) that our results are sound, statistically.
Complete step by step solution:
Confidence levels are expressed as a percentage (for example, a 95% confidence level). It means that should you repeat an experiment or survey over and over again, 95 percent of the time your results will match the results you get from a population (in other words, your statistics would be sound). Confidence intervals are your results and they are usually numbers.
We constructed a 95% confidence interval for an experiment that found the sample mean temperature for a certain city in August was $\overline{x}=100$, with a population standard deviation of $\sigma =17.50$. There were 40 samples in this experiment.
The $\alpha $-level is $\dfrac{1-.95}{2}=.025$.
The formula is $\overline{x}\pm \left( z\times \dfrac{\sigma }{\sqrt{n}} \right)$. Here n is the number of samples. z is from the standard distribution tables (in the reference), and is $1.96$for a CI of 95%.
So, $\overline{x}\pm \left( z\times \dfrac{\sigma }{\sqrt{n}} \right)=100\pm \left( 1.96\times \dfrac{17.5}{\sqrt{40}} \right)=100\pm 5.42=\left[ 94.58,105.42 \right]$.
Note:
For example, if we survey a group of pet owners to see how many cans of dog food, they purchase a year. We test our statistics at the 99 percent confidence level and get a confidence interval of (200, 300). That means you think they buy between 200 and 300 cans a year. We are super confident (99% is a very high level) that our results are sound, statistically.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)