High School

A teacher has a large container of blue, red, and green beads. She wants her students to estimate the proportion of red beads. Each student selects 50 beads, counts the number of red beads, and returns the beads to the container. One student sample has 15 red beads. The students are asked to construct a 95% confidence interval for the true proportion of red beads in the container. Are the conditions for inference met?

Answer :

The conditions for inference are met, as:

  • The sample is random.
  • There are at least 10 successes and 10 successes in the sample.

What are the conditions of inference for a confidence interval?

The conditions of inference for a confidence interval are given as follows:

  • Random sample.
  • Sample size large enough.

For a confidence interval of proportions, the large enough condition is described as follows:

  • At least 10 successes.
  • At least 10 failures.

For this problem, the numbers are given as follows:

  • 15 red beans -> 15 successes.
  • 35 non-red beans -> 35 failures.

Hence the conditions are met.

More can be learned about confidence intervals at https://brainly.com/question/30920932

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