Ch. 12 - Analysis of Variance

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 12 - Analysis of Variance

Problem 12.R.4

Chapter 12, Problem 12.R.4

Birth Weights The table below lists some of the same data used in the preceding exercise, but the seven days of the week are combined into weekday (Monday, Tuesday, Wednesday, Thursday, Friday) and weekend days (Saturday, Sunday). Also, the birth weights are converted to kilograms. What do you conclude?

Verified step by step guidance

Step 1: Organize the data into two groups: weekday and weekend birth weights for each hospital (Albany, Bellevue, Olean, Strong). This will help in comparing the two groups effectively.

Step 2: Calculate the mean birth weight for each group (weekday and weekend) for each hospital. Use the formula for mean:

Mean = \frac{\sum x}{n}

, where

x

represents individual birth weights and

n

is the number of observations.

Step 3: Compare the mean birth weights between weekdays and weekends for each hospital. Look for patterns or differences in the averages to identify any trends.

Step 4: Calculate the standard deviation for each group to measure the variability in birth weights. Use the formula for standard deviation:

SD = \sqrt{\frac{\sum (x - Mean)^{2}}{n}}

Step 5: Based on the calculated means and standard deviations, interpret the results. Discuss whether there is a significant difference in birth weights between weekdays and weekends, and what this might imply about the data.

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Key Concepts

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

Descriptive Statistics

Descriptive statistics summarize and describe the main features of a dataset. In this context, it involves calculating measures such as the mean, median, and range of birth weights for weekdays and weekends across different locations. Understanding these statistics helps in comparing the central tendencies and variations in birth weights between the two time periods.

Comparative Analysis

Comparative analysis involves evaluating two or more groups to identify differences or similarities. In this case, it requires comparing birth weights recorded on weekdays versus weekends across various locations. This analysis can reveal patterns or trends, such as whether birth weights tend to be higher or lower on specific days.

Data Interpretation

Data interpretation is the process of making sense of numerical data and drawing conclusions from it. In the context of the provided table, it involves analyzing the birth weight data to determine any significant differences between weekdays and weekends. This skill is crucial for making informed conclusions based on statistical evidence.

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Related Practice

Textbook Question

Bonferroni Test Shown below are weights (kg) of poplar trees obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the table below. The data are from a study conducted by researchers at Pennsylvania State University and were provided by Minitab, Inc. Also shown are partial results from using the Bonferroni test with the sample data.

a. Use a 0.05 significance level to test the claim that the different treatments result in the same mean weight.

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Textbook Question

In Exercises 1–4, use the following listed measured amounts of chest compression (mm) from car crash tests (from Data Set 35 “Car Data” in Appendix B). Also shown are the SPSS results from analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different car sizes have the same mean amount of chest compression.

Anova

a. What characteristic of the data above indicates that we should use one-way analysis of variance?

120

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Textbook Question

Interaction

b. If there does appear to be an interaction between gender and age bracket, how should we continue with the procedure for two-way analysis of variance?

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Textbook Question

Birth Weights Data Set 6 “Births” includes birth weights (g), hospitals, and the day of the week that mothers were admitted to the hospital. Using rows to represent the four hospitals (Albany Medical Center, Bellevue Hospital Center, Olean General Hospital, Strong Memorial Hospital), and using columns to represent the seven different days of the week, a two-way table has 28 individual cells. Using five birth weights for each of those 28 cells and using StatCrunch for two-way analysis of variance, we get the results displayed below. What do you conclude?

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Textbook Question

Gender and Age Bracket Based on the display included with Exercise 8, what are the final conclusions?

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Textbook Question

"Interaction

a. Based on the display included with the preceding exercise, what do you conclude about an interaction between gender and age bracket?

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