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Ch. 8 - Hypothesis Testing
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 8 - Hypothesis TestingProblem 8.5.1a
Chapter 8, Problem 8.5.1a

RESAMPLING
a. In general, what does it mean to “resample” the following data set consisting of wait times (minutes) of customers waiting in line for the Space Mountain ride at Walt Disney World: 50, 25, 75, 35, 50?

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Resampling refers to the process of repeatedly drawing samples from a given data set, either with or without replacement, to make statistical inferences or to estimate properties of the population. In this case, the data set consists of wait times: 50, 25, 75, 35, 50.
To resample with replacement, you would randomly select values from the original data set, allowing the same value to be chosen multiple times. For example, a possible resampled set could be {50, 50, 25, 75, 50}.
To resample without replacement, you would randomly select values from the original data set without repeating any value. For example, a possible resampled set could be {75, 50, 35, 25, 50}.
Resampling is often used in methods like bootstrapping (with replacement) to estimate the sampling distribution of a statistic, or in permutation tests (without replacement) to test hypotheses.
In this context, resampling the wait times could help estimate the variability of the mean or median wait time, or test hypotheses about the distribution of wait times.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Resampling

Resampling is a statistical technique that involves repeatedly drawing samples from a dataset and analyzing the results. This method is often used to estimate the distribution of a statistic (like the mean or variance) when the underlying population distribution is unknown. In the context of the given dataset, resampling could help assess the variability of wait times and provide insights into customer experiences.

Sampling Distribution

A sampling distribution is the probability distribution of a statistic obtained from a large number of samples drawn from a specific population. It describes how the statistic (e.g., sample mean) varies from sample to sample. Understanding sampling distributions is crucial for making inferences about the population based on sample data, particularly when resampling techniques are applied.
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Bootstrap Method

The bootstrap method is a specific resampling technique that involves taking repeated samples, with replacement, from the original dataset to estimate the sampling distribution of a statistic. This approach allows for the estimation of confidence intervals and hypothesis testing without relying on strong parametric assumptions. In the context of the wait times dataset, bootstrapping could provide a robust way to analyze the variability and reliability of the average wait time.
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Related Practice
Textbook Question

Finding Critical Values

In Exercises 17–20, refer to the information in the given exercise and use a 0.05 significance level for the following.


a. Find the critical value(s).

b. Should we reject H0 or should we fail to reject H0?


Exercise 16

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Textbook Question

Identifying H0 and H1

In Exercises 5–8, do the following:


a. Express the original claim in symbolic form.

b. Identify the null and alternative hypotheses.


Systolic Blood Pressure Claim: Healthy adults have systolic blood pressure levels with a standard deviation greater than 5 mm Hg. Sample data: Data Set 1 “Body Data” in Appendix B shows that for 300 healthy adults, the systolic blood pressure amounts have a standard deviation of 15.85 mm Hg.

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Textbook Question

Using Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.


a. Use the critical value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

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Textbook Question

Statistical Literacy and Critical Thinking

In Exercises 1–4, use the results from a Hankook Tire Gauge Index survey of a simple random sample of 1020 adults. Among the 1020 respondents, 86% rated themselves as above average drivers. We want to test the claim that more than 3/4 of adults rate themselves as above average drivers.


Null and Alternative Hypotheses and Test Statistic


a. Identify the null hypothesis and the alternative hypothesis.

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Textbook Question

Finding Critical Values

In Exercises 17–20, refer to the information in the given exercise and use a 0.05 significance level for the following.


a. Find the critical value(s).

b. Should we reject H0 or should we fail to reject H0?


Exercise 15

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Textbook Question

At Least As Extreme A random sample of 860 births in New York State included 426 boys, and that sample is to be used for a test of the common belief that the proportion of male births in the population is equal to 0.512.


a. In testing the common belief that the proportion of male babies is equal to 0.512, identify the values of p^ and p.

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