Homework Questions?
Section 9.2
Tests about a Population Proportion
Test Statistic
• A test statistic measures how far a sample statistic diverges
from what we would expect the null hypothesis 𝐻0 we true, in
standardized units. That is…
• 𝑡𝑒𝑠𝑡 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐 =
𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐−𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟
𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐
Mr. Suk & Basketball
• In a SRS of 50 free throws, Mr. Suk made 32.
• What is the test statistic?
• Find and interpret the p-value.
Significance Test
• State: What hypotheses do you want to test, and at what
significance level? Define any parameters you use.
• Plan: Choose the appropriate inference method. Check
conditions.
• Do: If the conditions are met, perform calculations.
• Compute the test statistic (z)
• Find the P-value
• Conclude: Interpret the results of your test in the context of
the problem.
One-Sample z Test for a
Proportion
• 𝑧=
𝑝−𝑝0
𝑝0 (1−𝑝0 )
𝑛
• Find the p-value by calculating the probability of getting a z
score this large or larger in the direction specified by 𝐻0
POTATOES again…
• If the producer determines that more than 8% of potatoes have
blemishes, the truck will be sent away. A supervisor selects a
SRS of 500 potatoes and an inspection reveals that 47 of the
potatoes have blemishes. Carry out a significance test at the
𝛼 = 0.10 level. What should the producer conclude?
• State:
• Plan:
POTATOES again…
• Do:
• Conclude:
Two-Sided Tests…Example
• A website says that 50% of high school students have never
smoked a cigarette. Trey wonders if this is true in his large, urban
high school. Trey selects a SRS of 150 students from his school and
90 of them say they have never smoked a cigarette. What should
Trey conclude? Give appropriate evidence to support your answer.
• State:
• Plan:
Trey…
• Do:
• Conclude:
How does this tie into
confidence intervals?
• In Chapter 8 we would have done a confidence interval to be
95% confident…do that for Trey’s school instead!
Homework
• Pg 562 (33, 35-38, 46-52, 54-60)
• Do 37, 38, and 52 as a class!