SCENARIO 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. -Referring to Scenario 9-9, state the alternative hypothesis for this study.

The answer of SCENARIO 9-9 The president of a university claimed...

SCENARIO 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 Scenario 9-9, the null hypothesis would be rejected.

The null hypothesis would not be rejected because the sample mean of 1,501 is not significantly lower than the population mean of 1,520 at a 5% significance level given the small sample size and standard deviation.

SCENARIO 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 Scenario 9-9, if these data were used to perform a two-tail test, the p-value would be 0.1254.

The p-value for a two-tail test is twice the p-value for a one-tail test. In this case, the p-value for a one-tail test is 0.0627, so the p-value for a two-tail test is 0.1254.

SCENARIO 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. -Referring to Scenario 9-9, what critical value should the president use to determine the rejection region?

The answer of SCENARIO 9-9 The president of a university claimed...

SCENARIO 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. -Referring to Scenario 9-9, which of the following best describes the Type I error? A) The president concludes that the mean SAT score of the entering students is lower than previous years when it is indeed not lower. B) The president concludes that the mean SAT score of the entering students is higher than previous years when it is indeed not higher. C) The president concludes that the mean SAT score of the entering students is not lower than previous years when it is indeed lower. D) The president concludes that the mean SAT score of the entering students is not higher than previous years when it is indeed higher.

A Type I error occurs when the president concludes that the mean SAT score of the entering students is lower than previous years when it is indeed not lower. In this case, the null hypothesis is that the mean SAT score of the entering students is equal to or higher than the previous years' mean SAT score. If the president rejects the null hypothesis based on the sample evidence and concludes that the mean SAT score is lower than previous years, but this conclusion is incorrect, he commits a Type I error. A Type I error is rejecting a true null hypothesis, which means concluding that there is a significant difference when there is actually no significant difference.

SCENARIO 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. -Referring to Scenario 9-9, which of the following best describes the Type II error? A) The president concludes that the mean SAT score of the entering students is lower than previous years when it is indeed not lower. B) The president concludes that the mean SAT score of the entering students is higher than previous years when it is indeed not higher. C) The president concludes that the mean SAT score of the entering students is not lower than previous years when it is indeed lower. D) The president concludes that the mean SAT score of the entering students is not higher than previous years when it is indeed higher.

A Type II error occurs when the null hypothesis is not rejected even though it is false. In this scenario, the null hypothesis is that the mean SAT score of the entering students is the same as previous years (i.e., the mean SAT score is 1520). The alternative hypothesis is that the mean SAT score is lower than previous years. Thus, if the president concludes that the mean SAT score is not lower than previous years (i.e., fails to reject the null hypothesis), when it is indeed lower, then it is a Type II error. So, option C is the correct answer.

SCENARIO 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. -Referring to Scenario 9-9, state the null hypothesis for this study.

The answer of SCENARIO 9-9 The president of a university claimed...

SCENARIO 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 Scenario 9-9, the null hypothesis would be rejected if a 10% probability of committing a Type I error is allowed.

The null hypothesis would be rejected if the p-value is less than the level of significance, which is 0.05 in this case. A 10% probability of committing a Type I error is equivalent to a level of significance of 0.10, which is greater than the p-value. Therefore, the null hypothesis would not be rejected if a 10% probability of committing a Type I error is allowed.

SCENARIO 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 Scenario 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 5% probability of incorrectly rejecting the true null hypothesis.

The sample size is small (n=20), and the sample mean (1501) is not significantly lower than the population mean (1520) given the standard deviation (53). A hypothesis test would likely not show a statistically significant difference at the 5% level.

SCENARIO 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. -Referring to Scenario 9-9, the population the president is interested in is: A) all entering students to all universities in the U.S this year. B) all entering students to his university this year. C) all SAT test centers in the U.S.this year. D) the SAT scores of all students entering universities in the U.S.this year .

The population the president is interested in is all entering students to his university this year, as indicated by the statement "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." This suggests that he is specifically referring to the entering class at his university.

SCENARIO 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 Scenario 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.

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 5% probability of incorrectly rejecting the true null hypothesis.

SCENARIO 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 Scenario 9-9, the president can conclude that the mean SAT score of the entering class this year is lower than previous years using a level of significance of 0.10.

The answer of SCENARIO 9-9 The president of a university claimed...

SCENARIO 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 Scenario 9-9, the null hypothesis would be rejected if a 1% probability of committing a Type I error is allowed.

The null hypothesis would be rejected if the p-value is less than the significance level. A 1% significance level is stricter than a 5% level, making it less likely to reject the null hypothesis.

Quiz 9: Fundamentals of Hypothesis Testing: One-Sample Tests

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