Confidence Interval

Question

Confidence interval is a range of value that we can surely believe to be true.
Can you give an example (numerical/explanation) to elaborate?

The above statement is to make sure that you do not comment or answer the above question with the definition

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TheDataMonk 55 years 3 Answers 897 views Grand Master 0

Answers ( 3 )

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    We measure the heights of 40 randomly chosen men, and get a mean height of 175cm,

    We also know the standard deviation of men’s heights is 20cm.

    The 95% Confidence Interval (we show how to calculate it later) is:

    175cm ± 6.2cm

    confidence interval 175 plus minus 6.2

    This says the true mean of ALL men (if we could measure all their heights) is likely to be between 168.8cm and 181.2cm.

    But it might not be!

    The “95%” says that 95% of experiments like we just did will include the true mean, but 5% won’t.

    So there is a 1-in-20 chance (5%) that our Confidence Interval does NOT include the true mean.

  2. Raahul
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    For example, the statement is that the confidence interval is (100,110) and the confidence level is 95%. t=This statement was obtained after we did a test using sample statistic. A z-value (or t-statistic in case we do not know the population variance and the sample is small), sample means, sample size and population variance are used to calculate the interval. It means that the population statistic lies between these 2 values and we are 95% confident that this statement is true.

  3. dhingra.13
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    Confidence Interval works with probability, probability of getting the exact value of the parameter in the specified range (confidence interval).
    We might have a 90% confidence interval specifying a 90% chance (probability) of obtaining the value of the parameter in the given range of values or a 95% confidence interval or even a 99% confidence interval. Interpretation remains the same with only change in the p[robability of occurrence of that event.
    Moreover, we cannot be 100% sure of an event until it is the exact value that we have been looking for. This never happens because we are not dealing with population data but sample data.

    For instance, we are doing research on the average height of a student in the age group of 10-15 years.
    Since we need to figure out the average height of a person in the age group of 10-15 years, we will consider few kids in the age group of 10-15 years and measure their height. This is the sample data that we are taking.
    Now, to find out a 95% confidence interval for getting the mean height (not the mean sample height) of a student, we will form a range of values that will take into account the probability of 95%. The range, thus obtained, ensures that the mean population height of a student in the age group of 10-15 years will lie in this interval itself with a probability of 0.95

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