John Wiley & Sons TI-83 User Manual download pdf (Page 86)

Our hypotheses are H0 : the median is at least $70 versus H1 : the median is less than $70. For

a large sample size (n = 89 households that were above or below $70) we can use 1-PropZTest.

The p-value is 0.084, which is greater than our significance level. We fail to reject the null

hypothesis, and believe that the median price is at least $70.

Medians of Paired Data

Given paired data, we can test to see if the medians of their respective populations are the same

by applying a signs test. If the medians were the same, then there if a 50% chance for one

measurement of a pair to be larger than the other. We can replace each pair by a sign indicating

whether the first or the second measurement is larger.

Example: Blood Pressure

A researcher wants to find the effect of a special diet on systolic blood pressure in adults. She

selected a sample of 12 adults and put them on this dietary plan for three months. The following

table gives the systolic blood pressure of each adult before and after the completion of the plan.

Before After

210 196

185 192

215 204

198 193

187 181

225 233

234 208

217 211

212 190

191 186

226 218

238 236

Using a 2.5% significance level, can we conclude that the dietary plan reduces the median

systolic blood pressure of adults? Our hypotheses are H0 : the diet does not reduce the median

systolic blood pressure of adults versus H1 : that it does. We begin by replacing the paired

data by signs indicating whether the Before or After pressure is larger:

+ − + + + − + + + + ++

We have ten +’s out of twelve signs. Since it is a right-tailed test, the p-value will be the

probability of getting ten or more successes out of twelve trials in a binomial experiment where p

= 0.5.

p-value = Pr(X _ 10)

= 1 − Pr(X _ 9)

= 1 − binomcdf(12, 0.5, 9)

= 0.019

1 2 ... 81 82 83 84 85 86 87 88 89

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John Wiley & Sons TI-83 User Manual Page 86