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**1 - 3**of**3**### STUDENTS ’ UNDERSTANDING OF CONFIDENCE INTERVALS

"... The aim of this study was to gain knowledge of students ’ beliefs and difficulties in understanding confidence intervals and to use this knowledge to develop improved teaching programs. This study took place over four consecutive teaching semesters of a one-semester tertiary statistics unit. The stu ..."

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The aim of this study was to gain knowledge of students ’ beliefs and difficulties in understanding confidence intervals and to use this knowledge to develop improved teaching programs. This study took place over four consecutive teaching semesters of a one-semester tertiary statistics unit. The study was cyclical, in that the results of each semester were used to inform the instructional design for the following semester. Over the semesters the following instructional techniques were introduced: simulation with and without a computer, encouraging students to write about their work, and the use of alternative representations. As the interventions progressed, a higher proportion of students successfully defined and used confidence intervals to estimate the value of the population mean. This study also identified sources of confusion for students that can be a basis for further research. This paper describes a study that examined students ’ problems in understanding confidence intervals for the mean in a first-year tertiary statistics unit and the results of an intervention that aimed to improve this understanding. Confidence intervals are used to estimate the values of population parameters. They give a range of plausible populations from which a random sample might produce the observed sample statistic.. One of the problems with statistical inference is that

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"... Building intuitions about statistical inference based on resampling ..."

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### Strategies Used by Students to Compare Two Data Sets

"... One of the common tasks of inferential statistics is to compare two data sets. Long before formal statistical procedures, however, students can be encouraged to make comparisons between data sets and therefore build up intuitive statistical reasoning. Such tasks also give meaning to the data collect ..."

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One of the common tasks of inferential statistics is to compare two data sets. Long before formal statistical procedures, however, students can be encouraged to make comparisons between data sets and therefore build up intuitive statistical reasoning. Such tasks also give meaning to the data collection students may do. This study describes the answers given by beginning university students to tasks involving comparing data sets in graphical form, originally designed for students between Grades 3 to 9. The results show that whereas all the students had successfully completed either pre-tertiary mathematics or a bridging mathematics course many had similar difficulties to students of a younger age. In particular, they did not use a measure of centre or proportional reasoning when appropriate. One of the common tasks in inferential statistics is to compare two data sets. For example, is one group faster than the other group? Does the new drug work better? In the formal procedures of inferential statistics, questions similar to these are often answered by comparing the values of the arithmetic mean of each group while taking into account the value of the standard deviation of each group. Using less formal means of making comparisons, however, students can compare two data sets by using a measure of centre such as the arithmetic mean or by using proportional reasoning. For students to use a measure of centre they need to know that this statistic is somehow representative of a group (Gal, Rothschild, & Wagner, 1990). Despite the wide spread use of the arithmetic mean (the average) in everyday applications, previous research has shown that students often only perceive the arithmetic mean as the learned algorithm. Because these students do not regard the arithmetic mean as a representative number they are generally unsuccessful in using it to make decisions about data (Mokros & Russell,