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19 December, 11:06

Leon wants to estimate the proportion of the seniors at his high school who like to watch football. He interviews a simple random sample of 50 of the 200 seniors on campus. He finds that 32 like to watch football. Is the random condition for finding confidence intervals met? Explain.

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  1. 19 December, 11:16
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    Yes, the random conditions are met

    Step-by-step explanation:

    From the question, np^ = 32 and n (1 - p^) = 18.

    Thus, we can say that:Yes, the random condition for finding confidence intervals is met because the values of np^ and n (1 - p^) are greater than 10.

    Also, Yes, the random condition for finding confidence intervals is met because the sample size is greater than 30.

    Confidence interval approach is valid if;

    1) sample is a simple random sample

    2) sample size is sufficiently large, which means that it includes at least 10 successes and 10 failures. In general a sample size of 30 is considered sufficient.

    These two conditions are met by the sample described in the question.

    So, Yes, the random conditions are met.
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