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Use the table to answer the question.

This table displays the number of 10th and 11th-grade students who prefer either hip-hop or pop.
Hip-Hop Pop Totals
10th Grade 112 53 165
11th Grade 98 147 245
Total 210 200 410
Examine the data from a survey of 10th and 11th graders about which music genre they prefer.

Using relative frequencies, which of the following is true?

(1 point)
Responses

If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.
If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.

If you are a 10th grader, you are more likely to prefer pop.
If you are a 10th grader, you are more likely to prefer pop.

If you like pop, you are more likely to be a 10th grader.
If you like pop, you are more likely to be a 10th grader.

If you are an 11th grader, you are more likely to prefer hip-hop.
pick 1st 2nd 3rd or 4th

1 answer

To assess the statements, we will compute the relative frequencies from the provided data in the table.

First, let's look at the relevant numbers:

Total students:

  • 10th Grade: 165
  • 11th Grade: 245
  • Total: 410

Relative Frequencies of Preferences:

  1. Hip-Hop:

    • 10th Grade: 112 / 165 = 0.6788 (approximately 67.88%)
    • 11th Grade: 98 / 245 = 0.4 (approximately 40%)

  2. Pop:

    • 10th Grade: 53 / 165 = 0.3212 (approximately 32.12%)
    • 11th Grade: 147 / 245 = 0.6 (approximately 60%)

Now, let's analyze each statement using these relative frequencies:

  1. If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.

    • This statement is false because about 67.88% of hip-hop listeners are 10th graders and only 40% are 11th graders.

  2. If you are a 10th grader, you are more likely to prefer pop.

    • This statement is false since 10th graders prefer hip-hop (67.88%) over pop (32.12%).

  3. If you like pop, you are more likely to be a 10th grader.

    • This statement is false because 60% of pop listeners are 11th graders (147 out of 245), while only 32.12% are 10th graders.

  4. If you are an 11th grader, you are more likely to prefer hip-hop.

    • This statement is false since a majority (about 60%) of 11th graders prefer pop, while only 40% prefer hip-hop.

Given the analysis of the data and the computations above, none of the statements are correct. If you must select one based on general trends observed from the data, it would be advisable to omit any choice since all provided options are not true. However, since this is not an option, the closest assessment might be to highlight the least false, but that would not be warranted in terms of accuracy.

If your intention is to select from only the given options and one has to engage with the distributed answers provided despite their inaccuracy, please note that the answers are all technically incorrect.

If forced to choose, one might consider the first option regarding hip-hop due to the larger size of the 10th-grade sample; however, it stands incorrect but for sheer probability stance in social settings.