#10 ### SAT Mathematics Score AnalysisThe mean SAT score in mathematics is 510, with a standard deviation of 43. A special preparation course claims its graduates have a mean SAT score, \( \mu \), greater than 510. An independent researcher samples 60 students from the course, finding a mean SAT score of 523. At a significance level of 0.05, we aim to determine if the population mean SAT score for course graduates exceeds 510. Assume the population standard deviation is also 43.#### Steps for Hypothesis Testing1. **State the Null and Alternative Hypotheses:** - \( H_0: \mu = 510 \) - \( H_1: \mu > 510 \)2. **Determine the Type of Test Statistic:** - Conduct a one-tailed test using a Z-test for the sample mean.3. **Calculate the Test Statistic:** - Use the formula for the Z-test statistic: \[ Z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}} \] - Where: - \( \bar{x} = 523 \) (Sample mean) - \( \mu = 510 \) (Population mean under \( H_0 \)) - \( \sigma = 43 \) (Population standard deviation) - \( n = 60 \) (Sample size) - Round the result to three or more decimal places.4. **Find the p-value:** - Use the standard normal distribution to find the p-value corresponding to the calculated Z value. - Round to three or more decimal places.5. **Conclusion:** - Determine if the p-value is less than or equal to 0.05. - If yes, reject the null hypothesis in favor of the alternative hypothesis.#### DecisionCan we support the preparation course's claim that the population mean SAT score is greater than 510?- **Options:** Yes / NoThis approach provides a systematic process for testing the claim about the SAT score improvement from the preparation course.

given data,n=60x¯=523α=0.05σ=43claim :μ>510one- tailed test

he mean SAT score in mathematics is 510. The standard deviation of these scores is 43. A special preparation course laims that the mean SAT score, μ, of its graduates is greater than 510. An independent researcher tests this by taking a andom sample of 60 students who completed the course; the mean SAT score in mathematics for the sample was 523. t the 0.05 level of significance, can we conclude that the population mean SAT score for graduates of the course is reater than 510? Assume that the population standard deviation of the scores of course graduates is also 43. erform a one-tailed test. Then complete the parts below. arry your intermediate computations to three or more decimal places, and round your responses as specified below. (If ecessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) F |x X 0 S p ca 010 0=0 OSO 020