Section 6.5 Tests for Proportions Monday, December 1, 2003

Tests for Proportions  Useful in analyzing qualitative data  Inference for a single proportion Sample proportion is the fraction of a sample that possesses a characteristic of interest “p-hat” or is used as sample proportion p is the population proportion Sample proportion is derived from an independent identical success/failure trials data-generating mechanism X=number of items in the sample with the characteristic of interest

Some Formulas

Hypotheses  Ho: p=#  Ha: p # or p ≠ #

Test Statistic

Confidence Interval for p

Confidence Interval

Example  Example 17, page 405 of text A series of experiments was conducted to find how to reduce the proportion of cells scrapped by a battery plant because of internal shorts. At the beginning of the study, about 6% of the cells produced were being scrapped. Among a sample of 235 cells made under a particular trial set of plant operating conditions, 9 cells had shorts. Is this significant evidence that less than 6% of cells have shorts?

Sample size estimation

Example (continued)  How large a sample is required to estimate the proportion of shorts in cells to within 1% with 95% confidence?

Assignment  Page 413 #1 and #3