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Transcript
Block 4 Seats
Block 5 Seats
Block 6
Warm-up
8.2 Testing a proportion
Answers to 8.1 E #11,12, 13, 14 and 16
Hypothesis Testing
8.2 Significance Test
Jenny and Maya wonder if heads and tails are equally likely
when a penny is spun. They spin pennies 40 times and get
17 heads.
Later… Miguel and Kevin spin pennies and get 10 heads out
of 40 spins for a sample proportion, p-hat of 0.25.
A sample proportion is said to be statistically significant if
it isn’t a reasonably likely outcome when the proposed
standard is true.
P-values
Instead of simply reporting whether a result is statistically
significant, it is common practice also to report a P-value.
The P-value for a test is the probability of seeing a result
from a random sample that is as extreme as or more extreme
than the result you got from your random sample if the null
hypothesis is true.
Find the P-value for Jenny and Maya. They spin pennies 40
times and get 17 heads.
A large P-value tells you that the sample proportion you
observed is near p0, so your result isn’t statistically significant.
Null and Alternative Hypothesis
The null hypothesis, H0, specifies a population model
parameter of interest and proposed a value for the
parameter.
Written as H0: parameter = hypothesized value
Spinning the coin we can hypothesize that H0: p = 0.5
The alternative hypothesis, HA, contains the values of the
parameter that we consider plausible if we reject the null
hypothesis. (written with ≠, <, or >)
The level of significance the p-value for which the null
hypothesis will be rejected. α - alpha
To reject or not to reject
In a courtroom, a defendant is either guilty or not
guilty. Notice they don’t say innocent.
Same with the null hypothesis.
Either reject the null hypothesis or fail to reject the
null hypothesis.
The rejection or lack of rejection is based on the p-value
and whether or not it is statistically significant.
Example: Finding Critical Values
Suppose you want to reject the null hypothesis when the
test statistic, z, is in the outer 10% of the standard normal
distribution—that is, with a level of significance equal to
0.10. What should you use as critical values? α = 0.1
Pg 498 Components of Significant Test
1. Give the name of the test and check the conditions for
its use. For a significance test for a proportion, three
conditions must be met: The sample is a simple random
sample from a binomial population. Both np0 and n(1
− p0) are at least 10. The population size is at least 10
times the sample size.
2. State the hypotheses, defining any symbols. When
testing a proportion, the null hypothesis, H0, isH0: The
percentage of successes, p, in the population from which
the sample came is equal to p0.The alternative
hypothesis, Ha, can be of three forms: p0  or p  or p 
Components continued…
3. Compute the test statistic, z, and find the critical
values, z*, and the P-value. Include a sketch that illustrates
the situation.
4. Write a conclusion. There are two parts to stating a
conclusion: Compare the value of z to the predetermined
critical values, or compare the P-value to . Then say
whether you reject the null hypothesis or don’t reject the
null hypothesis, linking your reason to the P-value or to
The critical values
H.W. and upcoming dates
Read all of 8.2, copy formulas and definitions.
After 2nd day of 8.2, there will be a quiz on 8.1 and
8.2 that will include questions about symbols,
formulas and vocabulary in addition to problems.
Know the steps for conducting a significance test.
Form A – Ch. 7 Test Common Mistakes
2. If two values are selected randomly and independently from two populations,
then which of these statements is not true?
A. The mean of the sampling distribution of the sum of the values is equal to the
sum of the population means.
B. The mean of the sampling distribution of the difference of the values is equal
to the difference of the population means.
C. The variance of the sampling distribution of the sum is equal to the sum of the
variances.
D. The variance of the sampling distribution of the difference is equal to the
difference of the variances.
E. If the two populations are normally distributed, so are the distributions of the
sum and the difference.
Related to 1 c. on the Practice Test and rules in Ch. 6 on variance and averages
Adding and Subtractin g
 X Y   X   Y

X Y
X  Y
 X2  Y   X2   Y2
 X2 Y   X2  
2
Y
Form A
2. A study measured the waist size of 250 men finding a mean of 36.33 inches and
a standard deviation of 4.02 inches. Here is the histogram of the measurements.
Form B
2.An investigator anticipates that the proportion of
red blossoms in his hybrid plants is 0.15. In a
random sample of 50 of his plants, 22% of the
blossoms are red. If the investigator anticipates the
correct proportion of red blossoms, the standard
error of the sampling distribution of the sample
proportion is approximately
A.0.051 B. 0.059
C. 2.52
D.2.93
E. cannot be determined
Form B
Choice for Statistics
• Extra day for
Review Friday and
Test on Tuesday
March 20th
• Quiz on Friday March 16th
• Tuesday Review, go over
quiz
• Test on Thursday March
22nd