(Solved): An SAT prep course claims to increase student scores by more than 60 points, on average. To test th ...

An SAT prep course claims to increase student scores by more than 60 points, on average. To test this claim, 9 students whio have previously taken the \( 5 A T \) are randorniy chosen to take the prep course. Their SAT scores before and after completing the prep course are listed in the following table. Test the claim at the \( 0.02 \) ievel of significance assuming that the population distribution of the paired differences is approximately normat. Let scores before completing the prep course be Population 1 and let scores after completing the prep course be Population 2 . Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. \[ \begin{array}{l} H_{\mathrm{e}} \div H_{a}=60 \\ H_{a}: H_{a} \quad 60 \end{array} \] Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimai paces We fail to reject the null hypothesis and conclude that there is insufficent e. support the cia \( \rightarrow \) that the SAT prep course increases atudent scores by mort We fail to reject the null hypsthesis and conclude that there is suif i ent ove support the cina that the Sal grep course increases rtudent seores by mse We reject the full hypother 1 and conciuce that there is suff tient widence the cim that the SkT Fres courie increases student scoret by more than 6 a We reject the nuil hyporthes i and conkiude that there is in1uff ciest evdente