TABLE 9-9
The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance.
-True or False: Referring to Table 9-9,the president can conclude that there is sufficient evidence to show that the mean SAT score of the entering class this year is lower than previous years with no more than a 10% probability of incorrectly rejecting the true null hypothesis.

Question

Quizplus · Accepted Answer

Using the one-sample t-test in Table 9-9 with a sample size of 20, a sample mean of 1,501, a population mean of 1,520, and a standard deviation of 53, the calculated t-value is -2.37. With a degrees of freedom of 19 and a 5% level of significance, the critical t-value is -2.093. Since the calculated t-value (-2.37) is less than the critical t-value (-2.093), we reject the null hypothesis that there is no difference between the mean SAT score of this year's entering class and the previous years' entering students. Therefore, we can conclude that there is sufficient evidence to show that the mean SAT score of the entering class this year is lower than previous years with no more than a 10% probability of incorrectly rejecting the true null hypothesis.

TABLE 9-9 The President of a University Claimed That the Entering Class