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Answer :
Final answer:
The hypothesis to be tested is whether the population mean (u) is equal to the sample mean (X_bar). To test these hypotheses, confidence intervals are calculated at different levels which indicate the range of values within which the population mean is expected to lie, with a certain level of confidence.
Explanation:
In statistics, when we want to test if the sample mean is significantly different from the population mean, we conduct a two-tailed hypothesis test. From the given problem, our null hypothesis (H0) would be that the population mean (u) is equal to the sample mean (X_bar), so u = 180 lbs. The alternative hypothesis (Ha) would be u ≠ 180 lbs. However, to test these hypotheses and infer something about the population from the sample, we calculate confidence intervals (CI) at different levels. Here, the confidence intervals provided (90%, 95%, and 99%) represent the range in which we would expect the population mean to lie, with a certain confidence. For instance, with a 90% confidence, we expect the population mean to lie between 181 and 186 lbs, and so on for the other confidence intervals.
Learn more about Hypothesis Testing and Confidence Intervals here:
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