Question

In: Statistics and Probability

The superintendent of a large school district speculated that high school students involved in extracurricular activities...

The superintendent of a large school district speculated that high school students involved in extracurricular activities had a lower mean number of absences per year than high school students not in extracurricular activities. She generated a random sample of students from each group and recorded the number of absences each student had in the most recent school year. The data are listed below. Test the superintendent’s claim at the α=.01 significance level. [To receive full credit, your response should be sure to state your hypotheses, check the relevant requirement(s), find a test value, find a critical value or p-value (either is OK), make your decision, and state your conclusion.]

Students in EC Activities: 4 1 2 0 5 6 2 1 0 3 0 1 1 4 8 6 9 2 0 4 2 10 5 6 1

Students not in EC Activities: 5 7 0 9 4 3 12 8 4 2 0 5 5 4 9 14 6 10 9 6 3

Solutions

Expert Solution

This is a sum of test of equality of means for two independent samples where the sample size for the first group is 25 and the second group is 21. The variance of the groups are unknown so we are using t test for unequal variance.

where is the mean number of absences of the students involved in EC activities and is the mean number of absences of the students not involved in EC activities.

This is a left tailed test

t-Test: Two-Sample Assuming Unequal Variances
Variable 1 Variable 2
Mean 3.32 5.952380952
Variance 8.56 13.44761905
Observations 25 21
Hypothesized Mean Difference 0
df 38
t Stat -2.655365953
P(T<=t) one-tail 0.005755783
t Critical one-tail 1.68595446
P(T<=t) two-tail 0.011511566
t Critical two-tail 2.024394164

where variable 1 denotes absences the students involved in EC activities and variable 2 denotes absences of students not involved in EC activities.

t test value is=-2.655365953

We are conducting the test at 1% level of significance. The calculated p value is 0.005755783 (one tailed value is considered as it is left tailed test)

Since the calculated p value 0.005755783 is less than 0.01 so null hypothesis is rejected.

So we may conclude what the superintendent had speculated  is probably correct i.e. the high school students who were involved in extracurricular activities had a lower mean number of absences per year than high school students not in extracurricular activities.


Related Solutions

(8 pts) The superintendent of a large school district speculated that high school students involved in...
(8 pts) The superintendent of a large school district speculated that high school students involved in extracurricular activities had a lower mean number of absences per year than high school students not in extracurricular activities. She generated a random sample of students from each group and recorded the number of absences each student had in the most recent school year. The data are listed below. Test the superintendent’s claim at the α=.01 significance level. [To receive full credit, your response...
In a school district, all sixth grade students take the same standardized test. The superintendent of...
In a school district, all sixth grade students take the same standardized test. The superintendent of the school district takes a random sample of 26 scores from all of the students who took the test. She sees that the mean score is 130 with a standard deviation of 7.2344. The superintendent wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 16. Is there evidence that the standard deviation of test scores has...
A new school district superintendent preparing to reallocate resources for physically impaired students wanted to know...
A new school district superintendent preparing to reallocate resources for physically impaired students wanted to know if the schools in the district differed in the distribution of physically impaired. The superintendent tested samples of 20 students from each of the five schools and found 5 physically impaired (and 15 unimpaired) students at School 1, 5 physically impaired (and 15 unimpaired) at School 2, 6 (and 14) at School 3, 4 (and 16) at School 4, and 7 (and 13) at...
A superintendent of a school district was requested to present to the school board demographic data...
A superintendent of a school district was requested to present to the school board demographic data based on the schools within the district. One item that the superintendent had to present was the percent of students who were eligible for free or reduced price lunch (a commonly used proxy for socio-economic status). The following percents were reported for the 40 schools in the district: 53.7 52.4 73.1 49.6 58.4 54.7 54.7 45.0 74.7 79.4 47.2 52.4 21.4 37.5 76.0 67.3...
In the last decade, only 50.4% of high school students in Tampa’s school district graduated high...
In the last decade, only 50.4% of high school students in Tampa’s school district graduated high school. Aiko believes her high school in St. Petersburg has a higher graduation rate. She collects a random sample of 54 former students of her high school and found that 33 of them graduated. Test Aiko’s belief using a significance level of 0.05.
A school district developed an after-school math tutoring program for high school students. To assess the...
A school district developed an after-school math tutoring program for high school students. To assess the effectiveness of the program, struggling students were randomly selected into treatment and control groups. A pre-test was given to both groups before the start of the program. A post-test assessing the same skills was given after the end of the program. The study team determined the effectiveness of the program by comparing the average change in pre- and post-test scores between the two groups....
(High school busing problem) The Arden County, Maryland, superintendent of education is responsible for assigning students...
(High school busing problem) The Arden County, Maryland, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to bus a certain number of students, for several sectors of the county are beyond walking distance to a school. The superintendent               partitions the county into three geographic sectors as he attempts to establish a plan that will minimize the total         number of student miles traveled by bus. He also...
To further examine the school performance scores of the district, the superintendent identified schools within the...
To further examine the school performance scores of the district, the superintendent identified schools within the district that could be matched to schools from surrounding districts using a series of demographic characteristics such as size, socio-economic status, and percent special education students. The data that were collected are presented below. School Pair 1 2 3 4 5 6 7 8 9 Superintendent School 70 73 70 73 82 72 70 82 75 Matched School 70 69 71 73 87 67...
The school district recently adopted the use of e-textbooks, and the superintendent is interested in determining...
The school district recently adopted the use of e-textbooks, and the superintendent is interested in determining the level of satisfaction with e-textbooks among students and if there is a relationship between the level of satisfaction and student classification. The superintendent selected a sample of students from one high school and asked them how satisfied they were with the use of e-textbooks. The data that were collected are presented in the following table. Table 1: Student Classification (N=128) Satisfied Freshman Sophomore...
The Drombostu district has recorded a 15% increase in the number of high school students in...
The Drombostu district has recorded a 15% increase in the number of high school students in the district that are not developed mental illness. The officer of the police service who disclosed this matter to the public has lamented the recent increases in the number of farms used to cultivate Indian hemp. But the police services are not ruling out other hereditary issues that may be accounting for this problem. There has not been a health center in the district...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT