To compare commuting times in various locations, independent...

To compare commuting times in various locations, independent random samples were obtained from the six cities presented in "The Morning Rush." The samples were from workers who commute to work during the 8: 00 a.m. rush hour. a. Construct a graphic representation of the data using six side-by-side dotplots. b. Visually estimate the mean commute time for each city and identify it with an X. c. Does it appear that different cities have different effects on the average amount of time spent by workers who commute to work during the morning 8: 00 a.m. rush hour? Explain. d. Does it visually appear that different cities have different effects on the variation in the amount of time spent by workers who commute to work during the morning 8: 00 a.m. rush hour? Explain.

To compare commuting times in various locations, independent random samples were obtained from the six cities presented in "The Morning Rush." The samples were from workers who commute to work during the 8: 00 a.m. rush hour.
a. Construct a graphic representation of the data using six side-by-side dotplots.
b. Visually estimate the mean commute time for each city and identify it with an X.
c. Does it appear that different cities have different effects on the average amount of time spent by workers who commute to work during the morning 8: 00 a.m. rush hour? Explain.
d. Does it visually appear that different cities have different effects on the variation in the amount of time spent by workers who commute to work during the morning 8: 00 a.m. rush hour? Explain.

Key Concepts

Measures of Variation

Measures of variation assess the spread or dispersion of data points within a group. Variation gives insight into the diversity or consistency of the data, and comparing these measures across groups allows one to determine if one group exhibits more variability in values than another, which is important for understanding the reliability and distribution of the central values.

Visual Inference in Statistics

Visual inference in statistics involves drawing conclusions about what the data might say by analyzing graphs and charts. This method relies on the human ability to detect patterns, trends, and differences across groups, and it aids in forming hypotheses about whether observed differences in central tendency and variation are significant before conducting further statistical tests.

Measures of Central Tendency

Measures of central tendency, such as the mean, provide a summary of the central or typical value in a data set. Estimating the mean from a graphical display, for instance by marking an 'X' on a dotplot, helps in comparing the central values across different groups and understanding the average conditions in each group.

Independent Random Samples

Independent random samples are selections of data points taken from different populations or groups in such a manner that each data point has an equal chance of being selected. This method minimizes bias and ensures that the samples are representative of their respective populations, thereby allowing reliable comparisons between groups.

Side-by-Side Comparison

Side-by-side comparisons involve placing multiple plots adjacent to one another, allowing for a direct visual comparison of different groups or categories. This technique is especially useful when assessing differences in central tendency and variation across groups, as it helps identify both similarities and distinctions in the data distributions.

Dotplot

A dotplot is a simple graphical display used to show the distribution of a small set of data points along a number line. Each dot represents a single data point, making it easy to observe clusters, gaps, and outliers, which helps in understanding the overall spread and distribution of the data set.

Transcript

00:01 In problem 37, we're going to be comparing the committing times in various locations.

00:07 And here we have six different cities in the united states.

00:12 And the first part of the question a will be constructing a box plot showing the six cities side by side.

00:21 And what we need to do first is to select the data.

00:24 And then you go to insert, then you press this bar here, and then you press this bar here, and then you press the box and whisker.

00:33 So this is the box plot for the data and each of these box plots represents the different cities.

00:41 Okay so in part b we're going to tell whether the box plot shows visual evidence suggesting that the city has an effect on the average morning or much time.

00:54 Now as you can see this box plot seem very similar and one of them shows any significant differences according to the graphical display.

01:07 So here we can make a conclusion that no, the graphs do not show visual evidence suggesting that the city has an effect on the average morning commute time.

01:19 Because each box plot looks about the same as the others.

01:24 And then we now move on to part b of the question, now part c of the question, where i'm supposed to use the analysis of variance technique to tell whether this data show sufficient evidence to claim that the city has an effect on the average morning commute time.

01:47 And here the level of significance alpha will be 0 .05.

01:56 So first we're going to move this chart aside and then we're going to use the analysis of variance tool on data and data analysis options.

02:09 So you press the analysis of variance single factor, then you select the data and then you make sure that it's grouped by the columns and the labels are in the first row and the alpha should be 0 .05.

02:32 Then for the output you can select a cell and you press okay and here are the results for the single factor analysis of variance.

02:49 Keep in mind that alpha level of significance is 0 .05...

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