The proportion of people who like playing basketball is 2%, so a student randomly sample 1000, but find the proportion is 4%, if the true proportion is 2%. What the probability that this student detect at least 4% in random sample?I used the formula, but found the z score is 4.51 which is impossible I think.

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Judovh0 · Accepted Answer

Your z-score is correct. We are conducting a test on a sample proportion, so the zscore under the hypotheses      H    0    :  p  =  .02        H    A    :  p  &amp;gt;  .02is                              p          ^                    −      p                                p          (          1          −          p          )                n              =            .04      −      .02                                .02          (          .98          )                1000                =  4.517This is indeed a high zscore, but it&#039;s not impossible. You might think it is strange because most tables in books don&#039;t have z score that go this high in the tables. It&#039;s true. You must use a computer program if your table doesn&#039;t carry z scores this high, or you could just report the probability as &quot;approximately zero&quot; should also be fine. The probability of detecting at least .04/getting a zscore of at least 4.517 is&amp;gt; 1-pnorm(4.517)[1] 3.136095e-06

The proportion of people who like playing basketball is 2%, so a student randomly sample 1000, but f

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