According to shopper data, 97% of households purchase toilet paper. An analyst believes this is too low. To investigate, the analyst selects a random sample of 500 households and finds that 98% of them purchase toilet paper. We found that we do not have convincing evidence at the α = 0.05 level to conclude that the true proportion of all households that purchase toilet paper differs from 0.97.The power of this test to reject p = 0.97 if 0.98 is true is 0.21. If the analyst were to decrease the significance level of the test, how would the power be affected?It would increase.It would decrease.It would remain the same.It would double.

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Arcatuert3u · Accepted Answer

*Type I error is denoted with  α  leve  i.e.,  α  level  = level of significanc  *Power of the test = 1 -   β  = 1 - Type II error   [i.e., Type II error =   β  ]Answer : Simply the answer is Option (B) - Power would decrease.Since, there is a direct positive relation between alpha level and power of test. As decreasing the significance level of the test then the power of the test would decreases. Likely, as increasing  the significance level of the test then the power of the test would increases.  i.e., When we decrease alpha   (  α  )  ,  we increase beta   (  β  )  and decrease the power of test  (  1  −  β  )  .Here, analyst were to decrease the significance level of the test. So, the power of test would decrease. Reason for wrong Answers :   Option A is not correct : Because, if we decrease the level of significance   (  α  )  it leads to increase the chances of making type II error   (  (  β  )  .  Thus by increasing alpha level, beta   (  β  )  value can increase not power of the test.Option C is not correct : Since, as changing level of significance accordingly the power of the test would be change. Thus, if decrease the significance level then power of the test would be decrease not remains same. Option D is not correct : Because, Analyst were to decrease the significance level of the test. So, the power of test would decrease not double. Hence, Option (B) - Power would decrease.

According to shopper data, 97% of households purchase toilet paper. An analyst believes this is too

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