A nutritionist believes that 10% of teenagers eat cereal for breakfast. To investigate this claim, she selects a random sample of 150 teenagers and finds that 25 eat cereal for breakfast. She would like to know if the data provide convincing evidence that the true proportion of teenagers who eat cereal for breakfast differs from 10%. Are the conditions for inference met?

A. Yes, the conditions for inference are met.
B. No, the 10% condition is not met.
C. No, the Large Counts Condition is not met.
D. No, the randomness condition is not met.

To determine if the data provide convincing evidence that the true proportion of teenagers who eat cereal for breakfast differs from 10%, we need to conduct a hypothesis test. The null hypothesis, denoted as H0, assumes that the true proportion is equal to 10%. The alternative hypothesis, denoted as Ha, assumes that the true proportion is not equal to 10%.

The conditions for inference in testing a claim about a proportion are as follows:

Random Sampling: The nutritionist selects a random sample of 150 teenagers, which satisfies the random sampling condition.
Independence: We assume that the teenagers in the sample are independent of each other, meaning that the choice of one teenager does not affect the choice of another teenager.
Success-Failure Condition: The success-failure condition states that both the number of successes (teenagers who eat cereal for breakfast) and failures (teenagers who do not eat cereal for breakfast) should be at least 10. In this case, the nutritionist found that 25 out of 150 teenagers eat cereal for breakfast, which satisfies the success-failure condition.

Based on the given information, the conditions for inference are met. Therefore, we can proceed with conducting the hypothesis test to determine if the data provide convincing evidence that the true proportion of teenagers who eat cereal for breakfast differs from 10%.

Learn more about testing a claim about a proportion here:

https://brainly.com/question/16147055

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