Textbook Question
Which statistic is the best unbiased estimator for μ?
a. s
b. xbar
c. the median
d. the mode
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3. Describing Data Numerically
Mean
2:02 minutesProblem 8.1.34e
Textbook Question
Putting It Together: Bike Sharing Bicycle sharing exists in a variety of cities around the country. Los Angeles has the Metro Bike Share system. Users pick up a bike from one station, go for a ride, and return the bike to any station. Go to www.pearsonhighered.com/sullivanstats and download the file 8_1_34. The data represent the duration (in minutes) of all rides in the fourth quarter (October through December) of 2018.
e. The column “Sample1” represents the duration (in minutes) of a simple random sample of 40 bike rides where the ride was a “Round Trip” (that is, return the bike to the same location it was rented from). What is the sample mean?
Verified step by step guidance1
Identify the data column labeled "Sample1" which contains the durations (in minutes) of the 40 bike rides that were round trips.
Recall that the sample mean is calculated by summing all the observed values in the sample and then dividing by the number of observations.
Write the formula for the sample mean: \(\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i\), where \(n\) is the sample size (40 rides) and \(x_i\) represents each individual ride duration.
Add together all the durations listed in the "Sample1" column to find the total sum of the ride durations.
Divide the total sum by 40 to compute the sample mean duration of the round trip rides.
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Simple Random Sample
A simple random sample is a subset of data selected from a larger population where each member has an equal chance of being chosen. This ensures the sample represents the population fairly, reducing bias and allowing valid inferences about the whole group.
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Sample Mean
The sample mean is the average value of a set of observations in a sample. It is calculated by summing all the data points and dividing by the number of observations, providing a measure of central tendency that estimates the population mean.
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Data Interpretation in Context
Understanding the context of data, such as ride durations for round trips, is essential for accurate analysis. It helps in correctly identifying relevant data columns and applying appropriate statistical methods to answer specific questions.
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