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

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

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

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

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

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

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

One Sample Z test for a population proportion

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

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

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

Calculating Test Statistic and P-Value

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

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

Question 1 In the Study of older students attitudes from exercise 1, the sample mean SSHA Score was 125.7 and the sample Standard Deviation was 29.8 a significance test yields a P-Value of 0.0101 Explain what it would mean for the null hypothesis to be true in this setting interpret the P-Value in context

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 125.7 or more

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.

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

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

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

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

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

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

Question 5 Answer C. Linear

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

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