A Gallup Poll Based On Telephone Interviews

A Gallop Poll That Was Based On Telephone Interviews Conducted April 9

A gallop poll that was based on telephone interviews conducted April 9-12, 2012, using a random sample of 1016 adults aged 18 and older, living in all 50 US states and the District of Columbia, indicated that 29% of Americans spent more money in recent months than they had spent in earlier months. But the majority (58%) still said that they enjoy saving money more than spending it.

a. Is 29% a statistic or a parameter? Explain.

b. Is 58% a statistic or a parameter? Explain.

What is the median for the following population data set?

Selected Answer: d. 3

Correct Answer: b. 1

Answer Feedback: Incorrect. Median position = (63 + 1) / 2 = 32; The 32nd car falls in the group with one defect, therefore the median = 1. I understand how you got the figure 32, but I can’t see how you concluded the median is 1 instead of 3. Could you please explain the calculation in more detail?

Paper For Above instruction

Introduction

Understanding the distinction between statistics and parameters is fundamental in data analysis. A statistic is a numerical summary derived from a sample, whereas a parameter is a similar measure based on an entire population. The survey or poll data, as presented, provides an opportunity to evaluate these concepts explicitly. This paper discusses whether the figures provided are statistics or parameters, explains the median calculation process for a data set, and clarifies the reasoning behind the median value determination.

Analysis of the Gallop Poll Data

The Gallop poll cited involved a random sample of 1016 adults out of the entire U.S. population. It indicated that 29% of respondents reported increased spending in recent months, and 58% preferred saving money over spending. Since these numbers are derived from a subset (sample) of the entire population, they are referred to as statistics. They serve as estimates of the complete population data, which would require surveying all Americans—an impractical task. Therefore, the 29% and 58% figures represent sample statistics because they are based on the sampled respondents rather than the entire population.

Parameters, in contrast, would relate to the proportions or measures calculated from the entire population of Americans. Since the poll only sampled a portion, and no data was collected from every individual in the population, these figures cannot be considered parameters. They are sample statistics used to infer population parameters, with the understanding that they approximate the true population figures. The distinction is essential because it impacts the interpretation and confidence levels associated with these estimates.

Understanding the Median Calculation

The second question in the assignment involves calculating the median of a given data set. The median is the middle value when the data are ordered from smallest to largest. To determine its position within a data set, one uses the formula: Median position = (n + 1)/2, where n is the total number of data points. For example, if the data set contains 63 observations, the median position is (63 + 1)/2 = 32. This indicates that the median is the 32nd value in the ordered list.

In a case where the data set includes groups or classes, the median is often estimated by identifying the group where the median position falls. In this particular example, the data likely consisted of counts of cars with certain defect numbers. The 32nd position falls within the group with a count of one defect, meaning the median number of defects per car in the population is 1. The confusion arises from interpreting the median value directly from the position rather than understanding how the position corresponds to the grouped data values.

Further Explanation of Median Calculation

In detail, the median calculation involves ordering the data, counting the total number of observations, and then finding the middle position. When the total number of observations is odd, the median is the value at the exact middle. When even, it is the average of the two middle values. In grouped data, the median often falls into a specific class interval, and interpolation methods are used to approximate its exact value. The key point is that the median position indicates the rank of the data point within the ordered list, which directly corresponds to the median value in the dataset.

Conclusion

In conclusion, the figures from the Gallop poll are sample statistics because they are based on a subset of the population. The explanation of the median value hinges on understanding the position formula and how it maps onto the dataset’s ordered values. Clarifying the median calculation helps prevent misconceptions and emphasizes the importance of precise interpretation when analyzing statistical data.

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