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Ch. 11 - Goodness-of-Fit and Contingency Tables
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. 11 - Goodness-of-Fit and Contingency TablesProblema 11.1.25a
Capitolo 11, Problema 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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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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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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Finding Standard Normal Probabilities using z-Table
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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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