On the SAT exam, a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the time allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed for students of this school to complete this portion of the exam. The conditions for inference are met. The test statistic is t = –1.85 and the P-value is between 0.025 and 0.05. What conclusion should be made at the significance level, ?Reject H0. There is convincing evidence that these students finished the exam in less than 25 minutes.Reject H0. There is convincing evidence that the true mean amount of time needed for students of this school to complete this portion of the exam is less than 25 minutes.Fail to reject H0. There is not convincing evidence that these students finished the exam in less than 25 minutes.Fail to reject H0. There is not convincing evidence that the true mean amount of time needed for students of this school to complete this portion of the exam is less than 25 minutes.

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Answered: On the SAT exam, a total of 25 minutes…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 26PFA

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On the SAT exam, a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the time allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses H₀: μ = 25 versus H_a: μ < 25, where μ = the true mean amount of time needed for students of this school to complete this portion of the exam. The conditions for inference are met. The test statistic is t = –1.85 and the P-value is between 0.025 and 0.05. What conclusion should be made at the significance level, ?

Reject H₀. There is convincing evidence that these students finished the exam in less than 25 minutes.

Reject H₀. There is convincing evidence that the true mean amount of time needed for students of this school to complete this portion of the exam is less than 25 minutes.

Fail to reject H₀. There is not convincing evidence that these students finished the exam in less than 25 minutes.

Fail to reject H₀. There is not convincing evidence that the true mean amount of time needed for students of this school to complete this portion of the exam is less than 25 minutes.

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