Question

in a discussion of SAT Mathematics (SATM) scores, someone comments: "Because only a select minority of California high school students take the test, the scores overestimate the ability of typical high school seniors. I think that if all seniors took the test, the mean score would be no more than 473." You do not agree with this claim and decide to use the SRS of 450 seniors to assess the degree of evidence against it Those 450 seniors had a mean SATM score of 485. Is this strong enough evidence to conclude that this person's claim is wrong at the 95% level? Assume standard deviation of scores is 95.

Answer 1

The z-score calculation for the hypothesis test shows that we cannot conclusively reject the claim that the mean SATM score is no more than 473 for all California seniors at the 95% confidence level. However, our sample has a higher mean, indicating the claim might not be accurate.

Step-by-step explanation:

To evaluate the claim about SAT Mathematics (SATM) scores, we use a hypothesis test to determine whether the sample mean score of 485 differs significantly from the hypothesized population mean score of 473. Given a standard deviation of 95 and a sample size of 450, we calculate the z-score.

The z-score is given by the formula:

z = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

z = (485 - 473) / (95 / sqrt(450)) ≈ 1.78

A z-score of 1.78 is less than the critical value of 1.96 for a 95% confidence level (two-tailed test). Therefore, we do not have enough evidence to reject the claim that the true mean score is no more than 473 at the 95% level. However, the sample mean is higher than 473, which suggests that the claim may not represent the true SATM abilities of the population of California high school seniors.