STA 291Fall 2009

Lecture 20Dustin Lueker

The p-value for testing H1: µ≠100 is p=.001. This indicates that…1. There is strong evidence that μ=1002. There is strong evidence that μ≠1003. There is strong evidence that μ>1004. There is strong evidence that μ<100

Example

2STA 291 Fall 2009 Lecture 20

The p-value for testing H1: µ≠100 is p=.001. In addition you know that the test statistic was z=3.29. This indicates that…1. There is strong evidence that μ=1002. There is strong evidence that μ>1003. There is strong evidence that μ<100

Example

STA 291 Fall 2009 Lecture 20 3

Range of values such that if the test statistic falls into that range, we decide to reject the null hypothesis in favor of the alternative hypothesis◦ Type of test determines which tail(s) the rejection

region is in Left-tailed Right-tailed Two-tailed

Rejection Region

4STA 291 Fall 2009 Lecture 20

Testing µ

◦ Without the aide of some type of technology it is impossible to find exact p-values when using this test statistic, because it is from the t-distribution

Test Statistic

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STA 291 Fall 2009 Lecture 20

An assumption for the t-test is that the population distribution is normal◦ In practice, it is impossible to be 100% sure if the

population distribution is normal It may be useful to look at histogram or stem-and-leaf plot

(or normal probability plot) to check whether the normality assumption is reasonable

Good news◦ t-test is relatively robust against violations of this

assumption Unless the population distribution is highly skewed, the

hypotheses tests and confidence intervals are valid However, the random sampling assumption must never be

violated, otherwise the test results are completely invalid

Normality Assumption

6STA 291 Fall 2009 Lecture 20

A courier service advertises that its average delivery time is less than 6 hours for local deliveries. A random sample of times for 12 deliveries found a mean of 5.6875 and a standard deviation of 1.58. Is this sufficient evidence to support the courier’s advertisement at α=.05?

State and test the hypotheses using the rejection region method

What would be the p-value if we used that method?

Example

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Thirty-second commercials cost $2.3 million during the 2001 Super Bowl. A random sample of 116 people who watched the game were asked how many commercials they watches in their entirety. The sample had a mean of 15.27 and a standard deviation of 5.72. Can we conclude that the mean number of commercials watched is greater than 15?

State the hypotheses, find the test statistic and p-value for testing whether or not the mean has changed, interpret◦ Make a decision, using a significance level of 5%

Example

8STA 291 Fall 2009 Lecture 20

Testing Difference Between Two Population Proportions Similar to testing one proportion Hypotheses are set up like two sample

mean test◦ H0:p1=p2

Same as H0:p1-p2=0

Test Statistic

9STA 291 Fall 2009 Lecture 20

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Government agencies have undertaken surveys of Americans 12 years of age and older. Each was asked whether he or she used drugs at least once in the past month. The results of this year’s survey had 171 yes responses out of 306 surveyed while the survey 10 years ago resulted in 158 yes responses out of 304 surveyed. Test whether the use of drugs in the past ten years has increased.

State and test the hypotheses using the rejection region method at the 5% level of significance.

Example

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