Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

2. Describing Data with Tables and Graphs

Frequency Distributions

Statistics

2. Describing Data with Tables and Graphs

Frequency Distributions

Previous problemNext problem

2:46 minutes

Problem 11.1.25a

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.

a. Enter the observed frequencies in the table above.

Verified step by step guidance

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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

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.

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.

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.

Watch next

Master Intro to Frequency Distributions with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

Tornado Alley Construct the relative frequency distribution corresponding to the frequency distribution in Exercise 1

Textbook Question

In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B

Frequency Distribution Construct a frequency distribution of the magnitudes. Use a class width of 0.50 and use a starting value of 1.00.

Textbook Question

In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B

[Image]

Frequency Distribution For the frequency distribution from Exercise 1, find the following.

a. Class limits of the first class

b. Class boundaries of the first class

c. Class midpoint of the first class

Textbook Question

Hershey Kisses Refer to Data Set 38 “Candies” and use the weights (grams) of Hershey’s Kisses. Begin with a lower class limit of 4.300 g and use a class width of 0.100 g. Does this distribution appear to be a normal distribution?

Textbook Question

What is the difference between a frequency polygon and an ogive?

Textbook Question

use the frequency distribution to find the (a) class width, (b) class midpoints, and (c) class boundaries.

Toledo, OH, Average Normal Temperatures (F)

Textbook Question

use the ogive to approximate

the number in the sample.

Textbook Question

Use the ogive to approximate

the height for which the cumulative frequency is 15.

Show more practices