Question

Height and bullying ~ In a study done in England, researchers collected data on 209 secondary school students. A student was categorized as short if he or she was below the third percentile for height at the beginning of the school year, but the researchers intentionally sampled in a way that made short students constitute almost half of the sample. Each student was also asked whether they had ever been bullied in school.

Among the 92 students categorized as short, 42 reported that they had been bullied in school.

Among the 117 students categorized as not short, 30 reported that they had been bullied in school.

We want to use statistical inference to determine if there is a difference in the proportions of short and not short students who report being bullied in school.

To use a normal distribution in this scenario, which of the following conditions must be satisfied?

	The observations within the short sample must be independent of each other.
	The observations within the not short sample must be independent of each other.
	The short sample and the not short sample must be independent of each other.
	There must be at least 10 students who reported that they had been bullied and at least 10 students who reported that they had not bullied in the short sample.
	There must be at least 10 students who reported that they had been bullied and at least 10 students who reported that they had not bullied in the non short sample.

Answer 1

The test procedure, called the two-proportion z-test, is appropriate when the following conditions are met:

• The sampling method for both the population is simple random sampling also
• The samples are independent in each group.
• The two groups are uncorrelated
• Each sample includes at least 10 successes and 10 failures.

Using the above assumptions we can conclude that all the conditions should be satisfied.