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Ch. 9 - Inferences from Two Samples
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. 9 - Inferences from Two SamplesProblema 20
Capitolo 9, Problema 20

In Exercises 17–24, use the indicated Data Sets from Appendix B. The complete data sets can be found at www.TriolaStats.com. Assume that the paired sample data are simple random samples and the differences have a distribution that is approximately normal.


Heights of Presidents Repeat Exercise 12 “Heights of Presidents” using all of the sample data from Data Set 22 “Presidents” in Appendix B.

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Step 1: Identify the paired sample data from Data Set 22 'Presidents' in Appendix B. Ensure that the data represents heights of presidents and is a simple random sample.
Step 2: Verify that the differences between paired samples have a distribution that is approximately normal. This can be done using graphical methods like a histogram or a normal probability plot, or by conducting a normality test such as the Shapiro-Wilk test.
Step 3: Calculate the differences between the paired sample data points. For each pair, subtract the height of one president from the height of the other to obtain the differences.
Step 4: Compute the mean and standard deviation of the differences. Use the formulas for mean (\( \text{Mean} = \frac{\sum x}{n} \)) and standard deviation (\( \text{SD} = \sqrt{\frac{\sum (x - \text{Mean})^2}{n-1}} \)) where \( x \) represents the differences and \( n \) is the number of pairs.
Step 5: Use the calculated mean and standard deviation of the differences to perform the required statistical analysis, such as constructing a confidence interval or conducting a hypothesis test, depending on the specific requirements of Exercise 12.

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Paired Samples

Paired samples refer to two sets of related data points where each observation in one sample is paired with a corresponding observation in the other sample. This design is often used in experiments where the same subjects are measured under different conditions, allowing for a direct comparison of the effects of those conditions.
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Sampling Distribution of Sample Proportion

Normal Distribution

Normal distribution is a probability distribution that is symmetric about the mean, indicating that data near the mean are more frequent in occurrence than data far from the mean. In statistics, many tests assume that the data follows a normal distribution, especially when sample sizes are small, as it allows for the application of various inferential statistical methods.
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Finding Standard Normal Probabilities using z-Table

Simple Random Sampling

Simple random sampling is a fundamental sampling technique where each member of a population has an equal chance of being selected. This method helps to ensure that the sample is representative of the population, reducing bias and allowing for valid statistical inferences to be made from the sample data.
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c. If the significance level is changed to 0.01, does the conclusion change?

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Clinical Trials of OxyContin OxyContin (oxycodone) is a drug used to treat pain, but it is well known for its addictiveness and danger. In a clinical trial, among subjects treated with OxyContin, 52 developed nausea and 175 did not develop nausea. Among other subjects given placebos, 5 developed nausea and 40 did not develop nausea (based on data from Purdue Pharma L.P.). Use a 0.05 significance level to test for a difference between the rates of nausea for those treated with OxyContin and those given a placebo.


a. Use a hypothesis test.

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Denomination Effect A trial was conducted with 75 women in China given a 100-yuan bill, while another 75 women in China were given 100 yuan in the form of smaller bills (a 50-yuan bill plus two 20-yuan bills plus two 5-yuan bills). Among those given the single bill, 60 spent some or all of the money. Among those given the smaller bills, 68 spent some or all of the money (based on data from “The Denomination Effect,” by Raghubir and Srivastava, Journal of Consumer Research, Vol. 36). We want to use a 0.05 significance level to test the claim that when given a single large bill, a smaller proportion of women in China spend some or all of the money when compared to the proportion of women in China given the same amount in smaller bills.


b. Test the claim by constructing an appropriate confidence interval.

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