An education minister would like to know whether students atGedrassi high school on average perform better at English or atMathematics. Denoting by ?1 the mean score for all Gedrassistudents in a standardized English exam and ?2 the mean score forall Gedrassi students in a standardized Mathematics exam, theminister would like to get a 95% confidence interval estimate forthe difference between the means: ?1 - ?2.
A study was conducted where many students were given astandardized English exam and a standardized Mathematics exam andtheir pairs of scores were recorded. Unfortunately, most of thedata has been misplaced and the minister only has access to scoresfor 4 students.
| Student | English | Mathematics |
| Student 1 | 80 | 66 |
| Student 2 | 75 | 70 |
| Student 3 | 75 | 66 |
| Student 4 | 76 | 66 |
The populations of test scores are assumed to be normallydistributed. The minister decides to construct the confidenceinterval with these 4 pairs of data points. This Student's tdistribution table may assist you in answering the followingquestions.
a)Calculate the lower bound for the confidence interval. Giveyour answer to 3 decimal places.
Lower bound =
b)Calculate the upper bound for the confidence interval. Giveyour answer to 3 decimal places.
Upper bound =
An assistant claims that there is no difference between theaverage English score and the average Math score for a student atGedrassi high school.
c)Based on the confidence interval the minister constructs, theclaim by the assistant can or cannot be ruledout.
