John Wiley & Sons TI-83 User Manual download pdf (Page 84)

Chapter

Nonparametric

Methods

Sign Test

The Sign Test is one of the most direct nonparametric methods; knowing nothing about the

distribution, we can still test claims about the median of a population because any sample

measurement stands a 50% chance of being above the median and a 50% chance of being below

the median. We can treat sample data as being a binomial experiment, with successes occurring

when the measurement is above the median. Similarly, to test if two alternatives are equally

likely, we treat our sample data as coming from a binomial experiment and compute the p-value

accordingly. In both cases we can test if the population proportion is 50%. We will use 1-

PropZTest for our p-value computations if n _ 25; otherwise we can fall back on binomcdf.

Example: Opposition to Shopping Mall

A developer is interested in building a shopping mall adjacent to a residential area. Before

granting or denying permission to build such a mall, the town council took a random sample of

75 adults from adjacent areas and asked them whether they favor or oppose construction of this

mall. Of these 75 adults, 40 opposed construction of the mall, 30 favored it, and 5 had no

opinion. Can you conclude that the number of adults who oppose construction of the mall is

higher than the number who favor it? Use a 1% significance level. Our hypotheses are H0 : p =

50% versus H1 : p > 50%, where p is the proportion of the population that opposed the mall’s

construction. We will only look at the data coming from respondents who had opinions, with n =

70. We use 1-PropZTest with x = 40 and n = 70. The p-value is 0.116, which is greater than our

significance level. We fail to reject the null hypothesis, and can not conclude on the basis of this

sample that there is more opposition than support for the construction of the mall.

Example: Median Price of Homes

A real estate agent claims that the median price of homes in a small town is $137,000. A sample

of 10 houses selected by a statistician produced the following data on their prices in dollars.

1 2 ... 79 80 81 82 83 84 85 86 87 88 89

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John Wiley & Sons TI-83 User Manual Page 84