Journal of Research in Innovative Teaching - National University

up to any convenient number as far as it does not result in an empty upper class. Therefore, it is
good to show two or more versions of breaking the same data set into a given number of classes.
Weighted mean. While solving problems on weighted mean, some students confuse the variable
(x) with the weight (w). Therefore, the instructor should put an emphasis on preventing such
errors.
Independent events. Students often overlook the fact that two events are dependent if event A
may be the cause of event B. It does not need to really cause event B.
Multiplication rule. Perhaps the most common stumbling block in applying this rule is the
probability of multiple occurrence of a specified versus unspecified event. Thus, the probability
of two randomly selected persons being born on a specific day of the week is 1/49, but the
probability of them being born on the same (unspecified) day of the week is 1/7. This difference
should be explained to the students by several examples. Incidentally, students grasp the concept
of selecting with or without replacement much easier.
The rule of at least one. This rule is especially important for learning discrete probability
distributions. A common error is confusing the probability of at least one and the probability of
exactly one. The students must be cautioned against this.
Counting. It goes without saying that the hardest thing for a student here is choosing the right
counting rule. The course shell contains a chart that guides the reader through this choice.
Nevertheless, confusing the Permutation and Combination rules is a frequent mistake. The
instructor should remind the students about it, especially before an exam.
Normal distributions. While students have a relatively easy time mastering the technique of
finding the area under the normal curve for a given z-score, they are often taken aback finding
the z-score for a given area. That happens mostly because the commonly used table of standard
normal distribution is designed for problems of the first type and is rather inconvenient for the
second. Meanwhile, it is not difficult to compose a table where the area serves as an entry and
the z-score is the outcome.
Confidence intervals. Most textbooks explain the techniques of constructing confidence intervals
but pay little or no attention to their applications. This may leave the learner with a feeling of
dissatisfaction with a result that seems ambiguous. It is important to show the students that
interval estimate may be more efficient than point estimate because it helps to choose the safer
decision. This can be demonstrated by examples such as the following:
Example 1. A dentist is going to open a new office in a small neighborhood. He ordered
research to find out how many times per year a resident sees a dentist and what the annual cost of
dental care per person is. The survey resulted in 95% confidence intervals (2.6, 3.2) for the
number of visits and ($415, $706) for the dental care cost.
(A) What number of visits must be taken into account to figure out the size of the office space
the dentist needs to rent
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