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Ch. 1 - Introduction to Statistics
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoTriola 14th EditionCh. 1 - Introduction to StatisticsProblema 1.1.23
Capitolo 1, Problema 1.1.23

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?

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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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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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Parameters vs. Statistics

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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Step 1: Write Hypotheses

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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Finding Standard Normal Probabilities using z-Table
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In Exercises 25–28, refer to the data in the table below. The entries are for five different years, and they consist of weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population [based on data from “The Trouble with QSAR (or How I Learned to Stop Worrying and Embrace Fallacy)” by Stephen Johnson, Journal of Chemical Information and Modeling, Vol. 48, No. 1].

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Conclusion If we were to use the sample data and conclude that there is a correlation or association between lemon imports and crash fatality rates, does it follow that lemon imports are the cause of fatal crashes?

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Quantitative/Categorical Data Identify each of the following as quantitative data or categorical data.


a. The platelet counts in Data Set 1 “Body Data” in Appendix B

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In Exercises 9–12, determine whether the sampling method appears to be sound or is flawed.


Nuclear Power Plants In a survey of 1368 subjects, the following question was posted on the USA Today website: “In your view, are nuclear plants safe?” The survey subjects were Internet users who chose to respond to the question posted on the electronic edition of USA Today.

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In Exercises 37–44, answer the given questions, which are related to percentages.

Marriage Proposals In a survey conducted by TheKnot.com, 1165 engaged or married women were asked about the importance of a bended knee when making a marriage proposal. Among the 1165 respondents, 48% said that the bended knee was essential.


a. What is the exact value that is 48% of 1165 survey respondents?

b. Could the result from part (a) be the actual number of survey subjects who said that a bended knee is essential? Why or why not?

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In Exercises 21–28, determine whether the study is an experiment or an observational study, and then identify a major problem with the study.

Atkins Weight Loss Program An independent researcher tested the effectiveness of the Atkins weight loss program by randomly selecting 1000 subjects using that program. Each of the subjects was called to report their weight before the diet and after the diet.

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In Exercises 29–36, identify what is wrong.

Cell Phones and Pirates In recent years, the numbers of cell phones and the numbers of pirates have both increased, so there is a correlation, or association, between those two variables. Therefore, pirates cause increases in cell phones.

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