Researchers in Philadelphia investigated whether pamphlets containing informatio

Question

Researchers in Philadelphia investigated whether pamphlets containing information for cancer patients are written at a level that the cancer patients can comprehend. They applied tests to measure the reading levels of 63 cancer patients and also the readability levels of 30 cancer pamphlets (based on such factors as the lengths of sentences and number of polysyllabic words) These numbers correspond to grade levels, but patient reading levels of under grade 3 and above grade 12 are not determined exactly. (a) Determine the median reading level of a patient and the median readability level of a pamphlet. (b) Does the closeness of these medians indicate that the pamphlets are well matched to the patients reading levels? Explain. (c) What proportion of the patients do not have the reading skill level necessary to read even the simplest pamphlet in the study?

Explanation / Answer

a) For median of reading levels, the total count is 63, therefore the median is the (63+1)/2 = 32nd value.
median = 9

For median of readability levels, the total count is 30, therefore the median is the average of 15th and 16th values.
median = (9+9)/2 = 9

b) The centers of the distributions are the same, but the distribution of patients’ reading levels are skewed to the left, while the pamphlets' readability levels are skewed to the right. This means the spreads are very different and many patients can’t read the simplest pamphlet. Therefore, no the pamphlets are not well matched to the paitents reading levls.

c) The simplest pamphlet has a readability level of 6, therefore the proportion is the number patients with reading levels <3, 3,4 and 5.

P(cannot read the simplest pamphlet) = (6+4+4+3)/63 = 0.2698

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