High School

Suppose the body weights of 20 to 29 years males have u=180 and o=40. We take an SRS of n=712 from this population and got = 183 lbs. We want to test if the sample mean is significantly different than the population mean. What do we hypothesize? Xtm > 2x640) 40 H, k=180 1833 FIR=15 What is our Cl at different level? 90% CI: 181 to 186 95% CI: 180 to 186 99% CI: 8010186

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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