11A/B

Null Hypothesis Forms Alternative Hypothesis Possible Forms
Proportions
Means
A glass of water
Results
Taste Test A 30 people participate.
17 prefer bottled water.
 Taste Test B 30 people participate.
21 prefer bottled water.
Results
Taste Test C 50 people participate.
22 prefer bottled water.
 Taste Test D 100 people participate,
44 prefer bottled water.
Results
Taste Test B 30 people participate.
21 prefer bottled water.
 Taste Test D 100 people participate.
44 prefer bottled water.
Sample size = 30

Standard error of  = 0.091

 A bar graph with a curve labeled “Sample Proportion p” on the x-axis. It is numbered in increments of 0.1 from 0.2 to 0.8. There is a peak at approximately 0.5.
Sample size = 100

Standard error of  = 0.050

  A bar graph with a curve labeled “Sample Proportion o” on the x-axis. It is numbered in increments of 0.1 from 0.2 to 0.8 with a peak at approximately 0.5.
Study Results Test Statistic
Taste Test B 30 people participate.
21 prefer bottled water.
 Taste Test D 100 people participate.
44 prefer bottled water.
Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Calculate and interpret standardized scores. 1–3
Use a normal distribution to describe the sampling variability of a sample proportion. 4–6
Identify sample size as a factor that affects precision in sampling. 7
Use the Empirical Rule to identify unusual values in a normal distribution. 8, 9

A bar graph labeled in increments of 0.1. There is a peak at approximately 0.16. A girl throwing plastic bottles in a bin outside.A bar graph labeled “Sample Proportion p” on the x-axis. It is numbered in increments of 0.1 from 0.3 to 0.8. There is at peak at approximately 0.57.A curve with a peak centered at approximately 0.5. The x-axis is labeled in increments of 0.05 from 0.35 to 0.65. A curve with a peak centered at approximately 0 and numbered in increments of 1 from -3 to 3 on the x-axis. The increments are also labeled in increments of sigma, with mu at 0.

Glossary 11A

conditional
assuming a certain condition has to be true.
null hypothesis
a baseline assumption about a population parameter of interest; what we assume to be true to begin with.
alternative hypothesis
what we consider to be plausible if the null hypothesis is false.

Glossary 11B

test statistic
a measure of the distance between the sample statistic and the null hypothesis value in terms of the standard error of the statistic.