on the sat exam, a total of 25 minutes is allotted for students to answer 20 math questions without the use…

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 $h_0: mu = 25$ versus $h_a: mu < 25$, where $mu$ = 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, $alpha = 0.01$?\nreject $h_0$. there is convincing evidence that these students finished the exam in less than 25 minutes.\nreject $h_0$. 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.\nfail to reject $h_0$. there is not convincing evidence that these students finished the exam in less than 25 minutes.\nfail to reject $h_0$. 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.

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 $h_0: mu = 25$ versus $h_a: mu < 25$, where $mu$ = 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, $alpha = 0.01$?\nreject $h_0$. there is convincing evidence that these students finished the exam in less than 25 minutes.\nreject $h_0$. 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.\nfail to reject $h_0$. there is not convincing evidence that these students finished the exam in less than 25 minutes.\nfail to reject $h_0$. 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.

Answer

Explanation:

Step1: Recall decision - rule for hypothesis testing

In hypothesis testing, if the P - value is less than the significance level $\alpha$, we reject the null hypothesis $H_0$. If the P - value is greater than or equal to $\alpha$, we fail to reject $H_0$.

Step2: Compare P - value and $\alpha$

We are given that $\alpha = 0.01$ and the P - value is between $0.025$ and $0.05$. Since the P - value (between $0.025$ and $0.05$) is greater than $\alpha=0.01$, we fail to reject the null hypothesis $H_0$.

Answer:

Fail to reject $H_0$. 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.