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&llll:::::::::&&&&&&Chapter 10 Outline
One and TwoSample Tests of Hypotheses
Statistical Hypotheses: General Concepts (pp. 284286)
Definition
D10.1 Statistical hypothesis: an assertion or conjecture concerning one or more populations
The Role of Probability in Hypothesis Testing
The Null and Alternative Hypotheses
Testing a Statistical Hypothesis (pp. 286293)
The Test Statistic
Definitions
Type I error (D10.2): Rejection of the null hypothesis when it is true
Type II error (D10.3): Acceptance of the null hypothesis when it is false
HYPERLINK "AlphaPvalue.pdf" The probability of a type II error
The HYPERLINK "AlphaBetaTradeOff.pdf" Role of (, (, and Sample Size
Illustration With a Continuous Random Variable
Important properties of a test hypothesis
Definition of Power (D10.4): Probability of rejecting Ho given that a specific alternative is true. 
One and Two Tailed Tests (pp.294295)
Definitions:
Onesided alternative > onetailed test
Twosided alternatives > twotailed test
How are the Null and Alternative Hypotheses Chosen?
HYPERLINK "CHAPTER10Examples.doc" Ex 10.1: Cereal brand ( 1sided)
HYPERLINK "CHAPTER10Examples.doc" Ex 10.2: 3bedroom homes proportion (2sided)
The Use of HYPERLINK "AlphaPvalue.pdf" pvalues for Decision Making (pp. 295 298
Preselection of a significance level
( = 0.10 vs ( = 0.05 vs ( = 0.01
A graphical Demonstration of a Pvalue
Definition of Pvalue (D10.5): is the lowest level )of significance) at which the observed value of the test is significant.
Pvalues vs Classic Hypothesis Testing 
Tests Concerning a Single Mean (pp. 300303)
Standardization of EMBED Equation.DSMT4
Test Procedure for a Single mean
HYPERLINK "CHAPTER10Examples.doc" Ex 10.3: death record (1 sided) 
HYPERLINK "CHAPTER10Examples.doc" Ex 10.4: Synthetic fishing line (2 sided)
Relationship to HYPERLINK "CInHypoRelation.pdf" Confidence Interval Estimation (pp. 303304)
Ho: ( = (o vs Ha: ( ( (o
reject Ho when (1  ()100% CI for ( does not include (o 
Tests on a Single Mean (Variance unknown) : pp. 304307
tstatistic for a test on a single mean
Comment on the SingleSample ttest (n < 30 vs n >30)
Annotated Computer printout for a SingleSample ttest (Minitab F10.2) 
Tests on Two Means (pp. 307312) book is very scanty. Read lab manual
Independent Means
Known population variances
Lab example
Unknown variances
Equal variances > can use pooled variance estimates
Ex 10.6 Abrasive wear of 2 laminated materials
Large Sample Tests 
Unequal variances, Equal sample sizes
Lab Example
Unequal variances, UnEqual sample sizes
Lab example
Paired Observations
Assumptions:
Ex 10.7 Forestry deer study
Annotated Computer Printout 
Tests on a Single Proportion (pp.324326)
Testing a proportion: small samples (pvalues approach only)
Ex 10.10 Heat pumps in Richmond (2 sided)
Testing a proportion: Large samples
Ex 10.11 Prescribed drug (1 sided)
Tests on Two Proportions
Pooled estimate of proportion p
Ex 10.12 Vote on proposed chem. Plant rural vs town (1 sided)

Chapter 10 Problem Solving
Guide to Procedures
Review problem
Quiz
Ch. 10.3. One and two tailed test.
EXAMPLE. A manufacturer of a certain brand of rice clams that the average saturated fat content does not exceed 1.5 grams. State EMBED Equation.3 and EMBED Equation.3 .
%Which population parameter?
%What is Manufacturer's claim? EMBED Equation.3
%What is my claim? EMBED Equation.3
Ch 10.5. Testing of a single mean (variance known).
EXAMPLE 10.3. A random sample of 100 recorded deaths in the USA during the past year showed an average life span of 71.8 years. Assuming a population standard deviation of 8.9 years and allowing only 5% chance of rejecting null hypothesis, when it is true, does this seem to indicate that the mean life span today is greater than 70 years?
EXAMPLE 10.4. A manufacturer of sport equipment has developed a new fishing line. He claims that mean breaking strength of 8 kg with standard deviation of 0.5 kg. A sample of 50 lines tested and found to have average breaking strength of 7.8 kg. Does this sample support the manufacturer's claim with significance level 1%?
Ch 10.7. Testing of a single mean (variance unknown).
EXAMPLE 10.5. The Edison Electric Institute has published figures on annual number of kilowatthours expended by various home appliances. It is claimed that a vacuum cleaner expends an average of 46 kilowatthours per year. If a random sample of 12 homes included in a study indicates that vacuum cleaners expend an average of 42 kilowatthours per year with a standard deviation of 11.9 kilowatthours, does this suggest at the 0.05 level of significance that vacuum cleaners expend, on average, less than 46 kilowatthours annually? What is the answer if the allowed probability of type I error is 15%? Assume the population to be normal.
Ch 10.8. Two samples: Test of Two Means.
EXAMPLE 10.6. An experiment was performed to compare the abrasive wear of two different materials. 12 pieces of material 1 and 10 pieces of material 2 were tested. The samples of material 1 gave an average wear of 85 units with standard deviation of 4 , while the samples of material 2 gave an average of 81 and standard deviation of 5. Can we conclude at the 0.05 level of significance that the abrasive wear of material 1 exceeds that of material 2 by more than 2 units? Assume the populations to be approximately normal with equal variances.
CH. 10. 11. Test on a single proportion.
%Which proportion?
EXAMPLE 10.11. A commonly prescribed drug for relieving nervous tension is believed to be only 60% effective. Experimental results with a new drug administrated to a random sample of 100 adults who were suffering from nervous tension show that 70 received relief. Is this sufficient evidence to conclude that the new drug is superior to the one commonly prescribed? Use a 0.05 level of significance.
CH. 10.12. Test on Two Proportions.
EXAMPLE 10.12. A vote is to be taken among the residence of a town and the surrounding county (region) to determine whether a proposed chemical plant should be constructed. To determine if there is a significant difference in the proportion of town voters and county voters favouring the proposal, a poll is taken. If 120 of 200 town voters favour the proposal and 240 of 500 county residence favour it, would you agree that the proportion of town voters favouring the proposal is higher than proportion of county voters? Allow 5% of type one error.
Additional problems.
Problem 1. To study the growth of pine trees at an early stage a worker records 40 measurements of the height of the one year old trees. It was found that sample mean is 1.715 cm. and standard deviation is 0.475 cm.
Q1. Do these data indicate that the mean height of the population is different from 1.9 cm at significance level of 0.05?
Q2. Is the evidence of your decision strong?
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