Data Set 3 in Appendix B includes a sample of 106 body...

Name: Problem 14, Chapter 8: Elementary Statistics
Uploaded: 2021-10-19T16:27:14-08:00
Duration: 4 min 51 s
Channel: Ajiboye Tunde
Description: Data Set 3 in Appendix B includes a sample of 106 body temperatures with a mean of 98.20 ° F and a standard deviation of 0.62 ° F. Use a 0.05 significance level to test the claim that the mean body temperature of the population is equal to 98.6 ° F, as is commonly believed. Is there sufficient evidence to conclude that the common belief is wrong?

Data Set 3 in Appendix B includes a sample of 106 body temperatures with a mean of 98.20 ° F and a standard deviation of 0.62 ° F. Use a 0.05 significance level to test the claim that the mean body temperature of the population is equal to 98.6 ° F, as is commonly believed. Is there sufficient evidence to conclude that the common belief is wrong?

Key Concepts

Null and Alternative Hypotheses

These are the foundational statements in statistical testing. The null hypothesis (H0) proposes that there is no difference or effect, while the alternative hypothesis (Ha) suggests that there is a significant difference or effect. In tests concerning means, H0 typically claims that the population mean is equal to a specific, hypothesized value, and Ha challenges this claim.

Significance Level (?)

This is the threshold used to determine whether to reject the null hypothesis. It represents the probability of committing a Type I error—rejecting the null hypothesis when it is actually true. Commonly set at 0.05, it implies a 5% risk of making such an error.

t-Test

The t-test is used to compare a sample mean to a hypothesized population mean when the population standard deviation is unknown. It is especially appropriate when dealing with small sample sizes. This test uses the t-distribution to calculate a test statistic, which then helps in assessing the evidence against the null hypothesis.

Test Statistic

In hypothesis testing, the test statistic is the standardized value calculated using the sample data. It quantifies how far the sample statistic (such as the sample mean) is from the hypothesized population parameter, taking into account the sample size and variability.

p-Value

The p-value represents the probability of obtaining test results at least as extreme as the observed data, assuming the null hypothesis is true. A small p-value indicates that the observed effect is unlikely to have occurred by chance, providing evidence against the null hypothesis.

Type I Error

This is the error made when the null hypothesis is rejected, even though it is true. The significance level (?) sets the risk of committing a Type I error. In hypothesis testing, minimizing this error is critical to ensure that any rejection of the null hypothesis is well justified.

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