Answer

Verified

371.4k+ 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.

Recently Updated Pages

What are the Advantages and Disadvantages of Algorithm

How do you write 0125 in scientific notation class 0 maths CBSE

The marks obtained by 50 students of class 10 out of class 11 maths CBSE

You are awaiting your class 10th results Meanwhile class 7 english CBSE

Which one of the following was not the cause of the class 10 social science CBSE

Which one of the following cities is not located on class 10 social science CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Mention the different categories of ministers in the class 10 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Who is the executive head of the Municipal Corporation class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which monarch called himself as the second Alexander class 10 social science CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Write an application to the principal requesting five class 10 english CBSE