1. Chapter 9 Testing A Claim
By: Amando, Devon, Sabrina, and Jorge

2. Null and Alternative Hypothesis
Null Hypothesis- the claim we weigh evidence against in a statistical test
The null typically has the statement “no difference” and the null is the claim that we seek evidence against
Alternating Hypothesis- the claim about the population that we are trying to find evidence for
Alternative deals with what we suspect to be true

3. P-Value
The probability computed assuming the null is true and the statistic would take a value as extreme as or more extreme than the one actually observed
Calculating P-Value will help us determine if we need to reject the null or if we fail to reject the null.
We determine if we reject the null or fail to reject the null based on our significance level or alpha

4. Alpha (significance level)
If P-Value is smaller than alpha we say that the results of a study are statistically significant at level alpha.
In this case we reject the null and conclude that there is convincing evidence in favor of the alternative hypothesis
If we fail to reject the null and conclude that there is not convincing evidence in favor of the alternative hypothesis
Alpha is assumed to be 0.05 unless told otherwise

5. Type 1 and Type 2 Error Type 1 error Type 2 Error
We reject the null when the null is true
Type 2 Error
We fail to reject null when the alternative is true

6. Significance test conditions
Random
The data were produced by a well designed random sample or randomized experiment
10%
When sampling without replacement check that the population is at least 10 times as large as the sample
Large Count
The sample is large enough to satisfy p>10 and n(1-P) greater than or equal to 10

7. The 4 Step Process for Significance Test
State: what hypothesis do you want to test and the significant level
Plan: Check the 3 conditions mentioned in the previous slide
Do: if the conditions are met then
Compute the Test Statistic
Find the P-Vaue
Conclude: make a decision about the hypothesis in the context of the problems

8. One Sample Z test for a population proportion

9. One Sample Z test for a population proportion (Calculator)
Stat, Test, 1-PropZTest
P0: is your Null
X: How many out of the sample are…..
N:Number in the sample
Prop: what the alternative will state (varies on if its one sided or two sided)
This will give you your Z and P value as well as P hat

10. Power
The power of a significance test against a specific alternative is the probability that the test will reject the null when the alternative is true
To find power you will use 1-P

11. Conditions For performing A significance Test about A Mean
Random
The data Came from a random sample
10%
When sampling without replacement check than it is greater than 10% of the entire population
Normal/Large Sample:
The population is greater than or equal to 30
If the distribution has a unknown shape then n has to be less than 30

12. Calculating Test Statistic and P-Value

13. Calculating Test Statistic and P-Value (Calculator)
2nd VARS, Distr, and Select tcdf
For lower your T Value
Upper will be a high number around 10,000
Df would be n-1
Calculations this would give you your P-Value

14. One Sample t Test for Mean (Calculator)
Input your values into L1
Stat Test T-Test
Input your values in the appropriate places
Will give you your values for T and P

15. Question 1
In the Study of older students attitudes from exercise 1, the sample mean SSHA Score was and the sample Standard Deviation was a significance test yields a P-Value of
Explain what it would mean for the null hypothesis to be true in this setting
interpret the P-Value in context

16. Question 1 Answer
The attitudes of older students do not differ from other students
If the population mean is equal to 115, then we have a chance f 1.01% of obtaining a random sample with a sample mean of or more

17. Question 2
The Survey of study Habits any attitudes (SSHA) in psychological test that measures students attitudes toward school and study habits. Score rage from 0 to 200. Higher scores indicate more positive attitudes. The mean score for U.S. College students is about 115. A teacher suspects that older students have a better attitudes toward school. She gives the SASHA to and SRS of 45 of over 1,000 at her college who are at least 30 years of age. Check the conditions for carrying out a significance test of the teacher‘s suspicion.

18. Question 2 Answer Random 10% Normal/Large Sample Was a SRS
The sample size (45) < 10% of the population size of 1,000
Normal/Large Sample
n=45 greater or equal to 30

19. Question 3
A test of Ho: P= 0.65 against Ha:P < 0.65 has test statistic Z= -1.78
What conclusion would you draw at the 5% significance level? At a 1% level?
If the alternative hypothesis were Ha: P not equal to 0.65, what conclusion would you draw at the 5% significance level? At the 1% level

20. Question 3 Answer
Reject Ho at the 5% significance level fail to reject Ho at the 1% significance level
Fail to reject Ho at both significance levels

21. Question 4 What is Type 2 Error?
Fail to reject the null when the the alternative is true
We reject the null when the alternative is true
Both the null and the alternative are wrong
Both the null and alternative are correct

22. Question 4 Answer
Fail to reject the null when the the alternative is true

23. Question 5
Which of the following are not a condition for preforming a significance test about a proportion?
Random
Large Count
Linear
10%

24. Question 5 Answer
C. Linear

25. Question 6
When checking for Normal/Large Sample in a significance test about the mean and has a Normal distribution which of the following is the right equation
N<30
N>30
N is greater or equal to 30
N does not equal 30

26. Question 6 Answer
C. N is greater than or equal to 30