AP Ch. 10 Day 3.notebook
March 28, 2011
Ch. 10 Day 3 (Section 2 & 3)
Hypothesis Testing
Writing a null hypothesis and an alternative hypothesis statement.
The null hypothesis, denoted by Ho: is a claim about a population characteristic that is initially assumed to be true.
The alternative hypothesis, denoted by Ha, is the competing claim.
In carrying out a test of Ho versus Ha, the hypothesis Ho is rejected in favor of Ha only if sample evidence strongly suggests that Ho is false. If the sample does not contain such evidence, Ho is not rejected. The two possible conclusions are then...
reject Ho or fail to reject Ho.
Mar 26­2:53 PM
Writing hypothesis statements.
Because of variation in the manufacturing process, tennis balls produced by a particular machine do not have identical diameters. Let μ denote the true average diameter for tennis balls currently being produced. Suppose that the machine was initially calibrated to achieve the design specification μ=3 in. However, the manufacturer is now concerned that the diameters are no longer conforming to this specification.
Write Ho & Ha in symbols and in words.
Ho :
Ha :
Mar 26­3:18 PM
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AP Ch. 10 Day 3.notebook
March 28, 2011
The Alternative Hypothesis has 3 options.
Ha: population characteristic > hypothesized value
Ha: population characteristic < hypothesized value
Ha: population characteristic ≠ hypothesized value
Mar 26­3:33 PM
How do you know if the data has a normal distribution, if it doesn't say that it is normal?
If n is large we can use the Central Limit Theorem (CLT)
How large is large? 40.
Mar 26­4:56 PM
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AP Ch. 10 Day 3.notebook
March 28, 2011
p­values
p­value: tells you the probability that the null hypothesis is true.
The smaller the p­value, the stronger the evidence is against Ho provided by the sample data.
p
Mar 26­3:55 PM
The Alternative Hypothesis has 3 options.
Ha: population characteristic > hypothesized value
(1­tail test)
Ha: population characteristic < hypothesized value
(1­tail test)
Ha: population characteristic ≠ hypothesized value
(2­tail test)
Mar 26­4:47 PM
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AP Ch. 10 Day 3.notebook
March 28, 2011
Significance level ∝
If the p­value is as small or smaller than alpha, we say that the data is/are statistically significant at level α=____ (decimal)
Example: if α=.05 ..... means we are requiring the data to be so strong that it would happen no more than 5% of the time when Ho is true.
For each pair, state whether the observed value leads to rejection of Ho.
α=.05
p=.084
α=.10
p=.084
α=.01
p=.033
α=.001
p=.003
α=.05
p=.498
α=.05
p=.049
α=.05
p=.05
Mar 26­4:00 PM
Inference Test ­ Shampoo
Bottles of a popular shampoo are suppose to contain 400ml. A manager suspects an employee has not set the filling machine correctly and is overfilling the bottles. The manager decides to randomly select 6 bottles and measure their contents. He finds that the bottles contain the following amounts of shampoo: 403, 402.3, 403.2, 399.7, 399.1 and 397.6 ml.
If the σ for all bottles filled is 1.5 ml, is this convincing evidence that the mean contents of the shampoo bottles is more than the advertised volume?
Mar 26­5:22 PM
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