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a) Calculate the standard error. Round your answer to four decimal places. b) Compute a test statistic to test the null hypothesis of

`H_(0):\mu =100`

. In any intermediate calculations, make sure you are using at least four decimal places. Round your FINAL answer to two decimal places. (Question ID: 831) Suppose you are conducting a hypothesis test for a difference in means and calculate a test statistic of 8.76. Based on this, which option gives the correct statistical decision and possible error? Reject

`H_(0)`

, we may have committed a Type I error. Reject

`H_(0)`

, we may have committed a Type II error. Fail to reject

`H_(0)`

, we may have committed a Type I error. Fail to reject

`H_(0)`

, we may have committed a Type II error. (Question ID: 2763) Why do smaller p-values provide stronger evidence against the null hypothesis than larger p-values? (Hint: Incorporate the definition of

`p`

-value into your answer).