Question

When discussing SAT mathematics scores for high school students in Texas, an educator states that the scores overestimate the math ability of high school seniors because only a select minority of students actually take the test. The educator believes that the mean score would be 495 if all high school seniors took the test. You believe the average would be higher and wish to test this claim using a hypothesis test.

You conduct a simple random sample of 100 high school seniors and find the mean score of the sample is 511. From previous studies of SAT scores, you believe the population standard deviation is σ=81.

1. At the α=0.01 level, test your claim that the mean score of seniors is higher than 495.
   1. (2 pts.) Give the null and alternate hypotheses for this problem.

2. (2 pts.) Find the critical value for this problem and sketch the critical region.

3. (2 pts.) Calculate the test statistic for this problem.

4. (2 pts.) Make your decision about the null hypothesis and summarize your results.

2. (2 pts.) If the significance level was α=0.05 , would this change your conclusion? Why or why not?

Answer 1

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