You obtain a dataset from a random sample. • You double-checked your dataset, and there were no typos, and no errors. • All cond

Question

3 years ago

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You obtain a dataset from a random sample. • You double-checked your dataset, and there were no typos, and no errors. • All cond

itions were met to develop a confidence interval. • You develop a 97% confidence interval for the population mean µ, and your confidence interval is 74.3 < µ < 78.3. • You double-checked your calculations, and everything was done correctly. Question: Later, you find out that the actual population mean is µ = 71. Why doesn’t your confidence interval contain the actual population mean?

Mathematics

1 answer:

Pepsi [2] · Answer 1 · 2022-03-17T16:46:59+03:00

Answer:

Interval is given with 97% confidence. Thus there is 3% probability that interval is not true.

Step-by-step explanation:

In Statistics, estimated intervals are given with some confidence level. In this example person develop the interval with 97% confidence.

<em>Statistically</em>, this means that the person can be 97% sure (not 100%) that population mean is 74.3 < µ < 78.3. There is still 3% probability that population mean falls outside of the interval.

Small sample size may also lead wrong estimates.