The band director at a high school wants to know what percentage of parents supports a decrease in the budget for fine arts. Because many parents attend the school’s annual musical, the director surveys the first 30 parents who arrive at the show. Explain why this sampling method is biased. Is the proportion of parents in the sample who support the decrease likely greater than or less than the proportion of all parents in the school who support the decrease?

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10-02-2022
Mathematics

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The band director at a high school wants to know what percentage of parents supports a decrease in the budget for fine arts. Because many parents attend the school’s annual musical, the director surveys the first 30 parents who arrive at the show. Explain why this sampling method is biased. Is the proportion of parents in the sample who support the decrease likely greater than or less than the proportion of all parents in the school who support the decrease?

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joaobezerra joaobezerra · Answer 1 · 2022-02-23T09:56:19+01:00

Using sampling concepts, it is found that the sampled is biased because only parents who attend the school's musical show are surveyed, hence they are not very likely to support the decrease, and the population proportion should be greater than the one found in the show.

How are samples classified?

Samples may be classified as:

Convenient: Drawn from a conveniently available pool.

Random: All the options into a hat and drawn some of them.

Systematic: Every kth element is taken.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.

A sample has to take into account all aspects of the population, otherwise it is biased. In this problem, either people support the decrease, or they do not. Only people that went to the show were surveyed, that is, people who are unlikely to support the decrease, which generates bias, as the population proportion should be greater than the one found in the show.

More can be learned about sampling concepts at https://brainly.com/question/25122507