CONFIDENCE INTERVAL

- A confidence interval is a statistical concept that provides a range of values within which we can be confident that the true value of a population parameter, such as the mean or proportion, falls with a certain level of probability. In simpler terms, it is a range of values that is likely to contain the true value of a parameter based on a given sample of data.

- The level of confidence typically expressed as a percentage, such as 95% or 99%, reflects the probability that the interval contains the true population value. The margin of error is also used to indicate the precision of the estimate. Confidence intervals are widely used in statistical inference to make statements about unknown population parameters based on sample data.

Solving the Question:

A large grocery store has been recording the number of shoppers that use coupons. Last year, 77% of shoppers used coupons. With a 95% confidence level, the manager found that the margin of error is 2.9%. What best describes the confidence interval?

To find the confidence interval, we use the formula:

[tex]\sf Confidence_{(Interval)} = Sample_{(Proportion)} \pm Margin_{(Error)}[/tex]

where:

• The sample proportion is 77% and the margin of error is 2.9%.

So, substituting these values, we get:

[tex]\sf Confidence_{(Interval)} = 0.77 \pm 0.029[/tex]

Now, we can calculate the lower and upper bounds of the confidence interval:

[tex]\sf Lower_{(Bound)} = 0.77 - 0.029 = 0.741[/tex]

[tex]\sf Upper_{(Bound)} = 0.77 + 0.029 = 0.799[/tex]

Therefore, the 95% confidence interval is from 74.1% to 79.9%. Hence, the best choice to describe the confidence interval is A. The 95% confidence interval is from 74.1% to 79.9%.

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