Scores on the SAT test are normally distributed with a mean = 500, and a standard deviation = 100. Dr. Ed Standards, the local district school superintendent, develops a new program, which he believes should increase SAT scores for students. He selects 25 local high school students to take the program and then take the SAT test. His sample has an average SAT score of 559. Conduct a hypothesis test to determine whether this program works. Show all of your steps and state all of your assumptions. Assume a = 0.05.

To determine whether the new program increases SAT scores, we can conduct a hypothesis test. First, state the null and alternative hypotheses. Next, calculate the standard error of the mean. Then, calculate the test statistic and compare it to the critical value.

Explanation:

To determine whether the new program increases SAT scores, we can conduct a hypothesis test. First, we state our null hypothesis that the program does not work, and our alternative hypothesis that the program does work. Next, we calculate the standard error of the mean using the formula: standard deviation / square root of sample size. Then, we calculate the test statistic using the formula: (sample mean - population mean) / standard error. Finally, we compare the test statistic to the critical value from the t-distribution to make a decision about our hypothesis.

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