AP STATISTICS
Chapter 10 – Introduction to Inference
Section 10.2: Tests of Significance
Name _______________________
Date __________
Period _____
Day 2 Assignment: Exercises 44, 45, 46, 47, 51, 55
A. Key vocabulary: test of significance, null hypothesis (H0), alternative hypothesis (Ha), p-value,
statistically significant at level , one-sided versus two-sided tests, inference toolbox (p. 571),
x  0
one-sample z test statistic, z 
, critical values, fixed sig. level z tests for a pop. mean (p. 578),
 n
confidence intervals and two-sided tests (p. 581), reject or not reject
B. Example: The Oregon Department of Fisheries suspects the fish in a lake are well below their target
mean length of 15”. Eryn, a wildlife biologist, obtained a representative sample of 124 Rainbow trout from
a lake. The sample mean length is 13.2” and standard deviation is 2.1”. She is very confident that the true
mean length of the fish in the lake is in the interval 12.83” to 13.57”, and that the fish are in fact below the
states targeted mean length of 15”.
A process you must have clear in your mind!
The states hypothesis is the research hypothesis, aka the alternative hypothesis. They believe the mean
length of the fish in the lake is less than 15”. They believe this: H a :  0  15 . But they need evidence to
support their belief. So, until the evidence is in they assume that the logical opposite of their research
hypothesis is true, i.e., that the mean length is 15” or more. They assume this is true: H 0 :  0  15 . This is
called the status quo or null hypothesis.
The question becomes this: How likely is it that a sample means like 13.2” (or ones even farther below
13.2”) happen when the actual population mean length is 15”? What needs to be done is an assessment of
the gap (as measured by standard deviations) between the supposed truth (15”) and the sample mean
(13.2”). If the gap is “small”, then the evidence tends to be not strong enough to reject the null hypothesis.
If the gap is “large”, then the evidence tends to be strong enough to reject the null hypothesis and conclude
that the research hypothesis is correct.
Inference Tool Box
Population: fish in the lake
Parameter: let x = the length to a fish in the lake
Check conditions: unbiased representative sample, lakes fish population is surely more than 10 times

sample size or 124 so okay to use  x  x , large n and CLT make normality assumption okay
n
Null hypothesis: H 0 :  0  15
Alternative hypothesis: H a :  0  15
Use a left-tailed one sample z test: z test statistic =
13.2  15
2.1 124
 9.54 with a p-value of nearly 0.
Conclusion in context: The z test stat is very large and the p-value is very small  it is highly unlikely that
a sample mean of 13.2” or less could happen if the population mean is in fact 15”. Reject the null in favor
of the alternative; there is strong evidence that the mean length of the fish in the lake is less than 15”.
Example: A manufacturer of Valentine’s Day chocolate candy claims the pieces in a box have an average
weight of one ounce. John buys a 16-piece box for his gal. He gets it home and it seems to be light. He
weighs the pieces and finds a sample average and standard deviation of 0.92 and 0.1 ounces, respectively.
Assuming the candy in the box is an unbiased (representative) sample from a normally distributed
population, John has a high level of confidence level that the manufacturers claim is untrue, but before he
causes a scene at the mall he decides to conduct a test of significance with =.01.
Do the test! Follow the Inference Toolbox (p. 571)
1. Identify the population of interest and the parameter you want to draw conclusions about. State the
null and alternative hypothesis.
2. Choose the appropriate inference procedure. Verify the conditions for using the selected procedure.
3. If the conditions are met, carry out the inference procedure. Calculate test stand and find p-value.
4. Interpret your results in the context of the situation.
Hypothesis test summary:



Describe the effect you are looking for in terms of a population parameter (like the mean ).
From the data, calculate a statistic like x that estimates the parameter.
The p-value says how likely a result at least as extreme as the one observed would be if the null
hypothesis were true.
Example of a two-sided test: Example 10.13 (pp. 573-574): Executive’s Blood Pressure
Example of a fixed significance level test: Example 10.14 (pp.578-579): Screen Tension
Example of using confidence interval for a test: Example 10.17 (p. 581): Screen Tension (again)