HIM 3200 Inference and Hypothesis Testing. Chapter Five Session Four Dr. Burton. Standard Deviation. Deductive/Inductive Reasoning. Deductive “to lead out from” General >>>>>>> specific If, then Inductive “to lead into” Specific>>>>>>>general. Math vs. Statistics.
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y = mx + b
A random variable related to the tested hypothesis.
Example: the total number of heads when a coin is tossed ten times or the difference between the mean percent reduction n serum cholesterol for the drug versus the placebo.
The probability of a type I error; denoted by
A set of values of the test statistic leading to rejection of the tested hypothesis; sometimes called the rejection region.
For example, 0, 1, 9, 10 heads or a percent difference equal to 5.
A set of values of the test statistic leading to acceptance of the tested hypothesis, that is the values of the test statistic not included in the critical region.
For example, 2,3,4,5,6,7,or 8 heads; any percent difference except 5.
The probability of rejecting the tested hypothesis when it is false, that is, when an alternative hypothesis is true; denoted by 1  where is the probability of a type II error.
The level of significance at which the observed value of the test statistic would just be significant, that is, would just fall into the critical region.
Truth
H0 True
H0 False
Type II
Error
Correct
results
Accept H0
Test
result
1 
Type I
Error
Correct
results
Reject H0
1 
Differences
H0 True = statistically insignificant
H0 False = statistically significant
Accept H0 = statistically insignificant
Reject H0 = statistically significant
1. State question in terms of:
H0: no difference or relationship (null)
Ha: is difference or relationship (alternative)
If I were to compare the final exam scores between the Summer session and the Fall session of HIM 3200 how would I state the null and alternative hypothesis?
1. State question in terms of:
H0: no difference or relationship (null)
Ha: is difference or relationship (alternative)
2. Decide on appropriate research design and statistic
Sometimes called the a priori alpha level.
Usually set at p = 0.05 (the probability of a Type I error)
1. State question in terms of:
H0: no difference or relationship (null)
Ha: is difference or relationship (alternative)
2. Decide on appropriate research design and statistic
3
2

+2
+3
+
Z scores
3
2
1
1
2
3
0
Probability
Upper tail .1587 .02288 .0013
Twotailed .3173 .0455.0027
What is the z score for 0.05 probability? (onetailed test)
1.645
What is the z score for 0.05 probability? (two tailed test)
1.96
What is the z score for 0.01? (onetail test)
2.326
What is the z score for 0.01 probability? (two tailed test)
2.576
= 113.1 + (1.96) (2.02)
= 113.1 + 3.96
= BETWEEN 113.1 –3.96 AND 113.1 + 3.96
= 109.1, 117.1 mmHg
Critical ratios are a class of tests
Critical ratio = parameter/SE of that parameter
t = difference between two means / SE of the difference between two means
z = difference between two proportions/SE of the difference between two proportions