Testing Population Mean Significance
A random sample of 27 observations from a large population has a mean of 22 and a standard deviation of 4.8. Can we conclude at that the population mean is significantly below 24?
This problem revolves around hypothesis testing, specifically testing a population mean when the sample size is small but sufficiently large to apply certain statistical techniques. In hypothesis testing for a population mean, we use a sample to make inferences about the larger population. Here, we assess whether the sample mean significantly deviates from a hypothesized population mean. This involves setting up a null hypothesis that the population mean is 24 and an alternative hypothesis that it is less than 24. A key aspect of solving this type of problem is determining the correct statistical test to employ. With the sample size being 27, and the population standard deviation unknown, the appropriate test here is the t-test for a population mean. This test allows you to see if the deviation of the sample mean from the population mean is statistically significant. Another important element is the significance level, alpha, set at 0.01, which denotes a 1% risk of rejecting the null hypothesis when it is actually true. A smaller alpha level indicates a stricter criterion for detecting statistical significance, implying stronger evidence is required to reject the null hypothesis.
Related Problems
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