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MAT10251 Statistical Analysis

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The proportion of Distinctions and High Distinctions in a unit can be used as a measure of an appropriate level and difficulty of assessment within the unit. It is usual that between 10% and 20% of students obtain Distinctions and High Distinctions. Therefore, to assess the level and difficulty of the revised assessment in this section the proportion of Distinctions and High Distinctions in STATS.101 will be estimated. Table 2.2 gives the PhStat2 output for a 90% confidence interval for the proportion of Distinctions and High Distinctions. Confidence Interval Estimate for the Proportion of Distinctions and High Distinctions Data Sample Size 75 Number of Successes 19 Confidence Level 90% Interval Lower Limit 0.1707 Interval Upper Limit 0.3359 Confidence Interval Table 2.2 From Table 2.2 it can be concluded that the proportion of Distinctions and High Distinctions is between 17.1% and 33.6%. Therefore, the proportion of Distinctions and High Distinctions may be within the usual range of 10% to 20%, however, the proportion may also be higher than 20%. The dichotomous mark distribution shown in Figure 2.1 and the uniform spread of marks from 50 to 80, indicate that a higher than normal proportion of High Distinctions and Distinctions could be expected. The uniform distribution also indicates that the assessment items are at the right level of difficulty, with most students who engage with the assessment items achieving at least a pass, and many able to achieve grades above a pass. 2 2.3 Exam Mark (2 marks) For students who complete a unit, the mean examination mark is an indication of the understanding of the average student and of the examination’s difficulty. A mean between 55% and 65% is desirable. If the mean is below 55% a sizable proportion of students will obtain a mark below the pass mark of 50% and a mean higher than 65% will result in the examination not easily distinguishing credit and higher students. Previously the mean examination mark for STATS.101 was 53.7% which is below the desirable range and it is hoped that the revised assessment has resulted in an increase in the mean mark. Therefore, the hypothesis that the revised assessment has resulted in an increase in the mean examination mark is tested in this section. Figure 2.3 gives the PhStat2 output of an upper tail hypothesis test to test if the mean examination mark is greater than the previous mean of 53.7%. t Test for Hypothesis of the Mean Null Hypothesis µ= 53.7 Level of Significance 0.1 Sample Size 65 Sample Mean 58.4846 Sample Standard Deviation 24.0636 t Test Statistic 1.6030 Upper-Tail Test Upper Critical Value 1.2949 p -Value 0.0569 Reject the null hypothesis STATS.101 Exam Mark Figure 2.3 From Table 2.3 the hypothesis that the mean examination mark for STATS.101 has not increased can be rejected at the 10% level of significance. Therefore, at this level of significance it can be concluded that the mean examination mark has increased from the previous mean of 53.7%, indicating that the revised assessment has resulted in an increase in examination mark.

MAT10251 Statistical Analysis

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