John Wiley & Sons TI-83 User Manual download pdf (Page 85)

Home Price

1 147,500

2 123,600

3 139,000

4 168,200

5 129,450

6 132,400

7 156,400

8 188,210

9 198,425

10 215,300

Using a 5% significance level, can we conclude that the median price differs from

$137,000?

Our hypotheses are H0 : the median price is $137,000 versus H1 : the median

price differs from $137,000. We replace the sample prices by signs: + if the price

is above the hypothetical median $137,000, and − if it is below.

Home Price

1 +

2 − 3 +

4 +

5 − 6 − 7 +

8 +

9 +

10 +

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

be twice the probability of getting seven or more successes out of ten trials in a

binomial experiment where p = 0.5.

p-value = 2 Pr(X _ 7)

= 2(1 − Pr(X _ 6)

= 2(1 − binomcdf(10, 0.5, 6))

= 2(1 − 0.828)

= 0.344

Since the p-value is greater than our significance level 5%, we fail to reject the

null hypothesis. The data does not lead us to conclude that the median differs

from $137,000.

Example: Median Phone Bill

A long-distance phone company believes that the median phone bill (for long distance calls) is at

least $70 for all the families in New Haven, Connecticut. A random sample of 90 families

selected from New Haven showed that the phone bills of 51 of them were less than %70 and 38

of them were more than $70, and 1 family had a phone bill of exactly $70. Using a 1%

significance level, can you conclude that the company’s claim is true?

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John Wiley & Sons TI-83 User Manual Page 85