Each Month The Us Census Bureau Mails Survey Forms To 250000 U

Each month, the U.S. census bureau mails survey forms to 250,000 U.S. households asking questions about the people living in the household and about such things as motor vehicles and housing costs. Telephone calls are made to households that don’t return the form. In one month, responses were obtained from 240,000 of the households contacted. The sample is A. all U.S. households. B. the 240,000 households that respond.

C. the 250,000 households initially contacted. D. the 10,000 households that did not respond. When you look up a z-score in table A, the number returned from the table is the A. cumulative proportion. B. number of individuals with that z-score. C. area under the curve to right of z. D. area under the curve between -z and z.

The given scenario involves understanding sampling and statistical concepts related to survey methodology and z-scores, which are fundamental in inferential statistics. The ability to identify the correct sample in a survey context and interpret z-scores accurately are crucial skills for analyzing data and making valid inferences.

Paper For Above instruction

The situation described pertains to the use of sampling in survey research, particularly in the context of the U.S. Census Bureau's efforts. The Bureau mails survey forms to 250,000 households each month to gather data about household demographics, economic status, and other relevant variables. It then follows up with telephone calls to households that do not return the survey forms. In the specific case mentioned, responses were received from 240,000 households, out of the 250,000 initially contacted. This leads to the question of what constitutes the sample in this context.

The concept of a sample in statistics refers to a subset of a population that is used to estimate or infer information about the entire population. In this scenario, although the survey involves initially contacting 250,000 households, the meaningful data used for analysis come from those households that responded. Therefore, the sample consists of the actual responding households, which in this case is 240,000. The initial contact group, 250,000 households, is considered the sampling frame—the larger population from which the sample is drawn—but the sample itself is the responding subset.

Hence, the correct answer to the question regarding what constitutes the sample is option B: the 240,000 households that responded. This reflects standard statistical practice, where the sample comprises observed data points that are used for analysis, regardless of how many were initially contacted.

The second part of the question pertains to the interpretation of z-scores when consulting statistical tables, specifically "table A." In statistics, a z-score indicates how many standard deviations a data point is from the mean in a standard normal distribution. When looking up a z-score in a standard normal table, the value returned typically represents the cumulative distribution function (CDF) for the standard normal distribution at that z-score.

This value, often called the cumulative proportion or cumulative probability, is the area under the curve to the left of the z-score. This interpretation is essential because it allows statisticians to determine the probability that a randomly selected value from a normal distribution is less than a given z-score. In most standard z-tables, the number reported is the area to the left of the z-score, meaning the probability that a value is below that z-score in the distribution.

Therefore, the correct answer to what the number returned from a z-table is—when looking up a z-score—is option A: cumulative proportion. This understanding of the cumulative proportion is fundamental in hypothesis testing, confidence interval construction, and other inferential procedures in statistics.

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