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Ch. 11 - Goodness-of-Fit and Contingency Tables
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 11 - Goodness-of-Fit and Contingency TablesProblem 11.1.25a
Chapter 11, Problem 11.1.25a

Testing Goodness-of-Fit with a Normal Distribution Refer to Data Set 1 “Body Data” in Appendix B for the heights of females.


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a. Enter the observed frequencies in the table above.

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1
Step 1: Review the provided table and identify the height intervals: 'Less than 155.45', '155.45 – 162.05', '162.05 – 168.65', and 'Greater than 168.65'. These intervals will be used to categorize the observed frequencies.
Step 2: Refer to Data Set 1 'Body Data' in Appendix B to extract the heights of females. Count the number of observations that fall into each height interval.
Step 3: For each interval, tally the observed frequencies by counting how many data points fall within the specified range. For example, count all heights less than 155.45 for the first interval.
Step 4: Enter the observed frequencies into the table under the 'Frequency' row corresponding to each height interval.
Step 5: Verify the total frequency by summing up the values entered in the table to ensure it matches the total number of observations in the data set.

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Key Concepts

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

Goodness-of-Fit Test

A goodness-of-fit test is a statistical hypothesis test used to determine how well a sample distribution fits a theoretical distribution. In this context, it assesses whether the observed frequencies of female heights align with the expected frequencies under a normal distribution. This test helps to evaluate the appropriateness of the normal model for the given data.
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Step 2: Calculate Test Statistic

Observed Frequencies

Observed frequencies refer to the actual counts of occurrences in each category of a dataset. In the context of the question, these frequencies represent the number of females whose heights fall within specified ranges. Accurately entering these observed frequencies is crucial for conducting the goodness-of-fit test and comparing them against expected frequencies.
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Creating Frequency Polygons

Normal Distribution

A normal distribution is a continuous probability distribution characterized by its bell-shaped curve, defined by its mean and standard deviation. It is significant in statistics because many real-world phenomena, including human heights, tend to follow this distribution. Understanding the properties of normal distribution is essential for interpreting the results of the goodness-of-fit test.
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Related Practice
Textbook Question

Questions 6–10 refer to the sample data in the following table, which describes the fate of the passengers and crew aboard the Titanic when it sank on April 15, 1912. Assume that the data are a sample from a large population and we want to use a 0.05 significance level to test the claim that surviving is independent of whether the person is a man, woman, boy, or girl.



Given that the P-value for the hypothesis test is 0.000 when rounded to three decimal places, what do you conclude? What do the results indicate about the rule that women and children should be the first to be saved?

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Textbook Question

Cybersecurity The table below lists the frequency of leading digits of Internet traffic interarrival times for a computer, along with the percentages of each leading digit expected with Benford’s law.


a. Identify the general notation used for observed and expected values.


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Textbook Question

Cybersecurity The table below lists the frequency of leading digits of Internet traffic interarrival times for a computer, along with the percentages of each leading digit expected with Benford’s law.


b. Identify the observed and expected values for the leading digit of 2.


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Textbook Question

Does the Treatment Affect Success? The following table lists frequencies of successes and failures for different treatments used for a stress fracture in a foot bone (based on data from “Surgery Unfounded for Tarsal Navicular Stress Fracture,” by Bruce Jancin, Internal Medicine News, Vol. 42, No. 14). Use a 0.05 significance level to test the claim that success of the treatment is independent of the type of treatment. What does the result indicate about the increasing trend to use surgery?



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Textbook Question

Testing Goodness-of-Fit with a Normal Distribution Refer to Data Set 1 “Body Data” in Appendix B for the heights of females.


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b. Assuming a normal distribution with mean and standard deviation given by the sample mean and standard deviation, use the methods of Chapter 6 to find the probability of a randomly selected height belonging to each class.

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Textbook Question

Weather-Related Deaths For the most recent year as of this writing, the numbers of weather-related U.S. deaths for each month were 61, 14, 22, 26, 29, 42, 93, 49, 47, 35, 96, 16, listed in order beginning with January (based on data from the National Weather Service). Use a 0.01 significance level to test the claim that weather-related deaths occur in the different months with the same frequency. Provide an explanation for the result.

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