1. Intro to Stats and Collecting Data
Intro to Stats
2:33 minutesProblem 1.1.23
Textbook Question
In Exercises 21–24, refer to the sample of body temperatures (degrees Fahrenheit) in the table below. (The body temperatures are from Data Set 5 in Appendix B.)
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Conclusion Given the body temperatures in the table, what issue can be addressed by conducting a statistical analysis of the data?
Verified step by step guidance1
Identify the research question or hypothesis that can be addressed using the sample of body temperatures. For example, you might want to determine if the average body temperature in the sample is significantly different from the commonly accepted average body temperature of 98.6°F.
Choose an appropriate statistical test to analyze the data. Since you are dealing with a sample mean and comparing it to a known value, a one-sample t-test could be suitable if the sample size is small and the population standard deviation is unknown.
Check the assumptions of the chosen statistical test. For a one-sample t-test, ensure that the body temperature data is approximately normally distributed. This can be assessed using graphical methods like a histogram or a Q-Q plot.
Calculate the test statistic using the formula for the one-sample t-test: \( t = \frac{\bar{x} - \mu}{s/\sqrt{n}} \), where \( \bar{x} \) is the sample mean, \( \mu \) is the population mean (98.6°F), \( s \) is the sample standard deviation, and \( n \) is the sample size.
Determine the p-value associated with the calculated test statistic and compare it to a significance level (commonly 0.05) to decide whether to reject or fail to reject the null hypothesis. This will help you conclude if the average body temperature in the sample is significantly different from 98.6°F.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Descriptive Statistics
Descriptive statistics involve summarizing and organizing data to understand its main features. This includes calculating measures such as mean, median, mode, and standard deviation. In the context of body temperatures, descriptive statistics can help identify the average temperature and the variability within the sample, providing a foundation for further analysis.
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Hypothesis Testing
Hypothesis testing is a statistical method used to make inferences or draw conclusions about a population based on sample data. It involves formulating a null hypothesis and an alternative hypothesis, then using statistical tests to determine the likelihood of the observed data under the null hypothesis. For body temperatures, hypothesis testing could address whether the average temperature significantly differs from a known standard, such as 98.6°F.
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Normal Distribution
The normal distribution is a continuous probability distribution characterized by a symmetric, bell-shaped curve. Many biological variables, including body temperature, are assumed to follow a normal distribution. Understanding this concept is crucial for applying certain statistical tests and for making inferences about the population from which the sample is drawn, as many tests assume normality in the data.
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