STA 291SPRING 2010

Lecture 20Dustin Lueker

A 95% confidence interval for µ is (96,110). Which of the following statements about significance tests for the same data is true?

1. When testing H1: μ≠100, p-value>.052. When testing H1: μ≠100, p-value<.05

Example

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Testing µ with n small

◦ Just like finding a confidence interval for µ n small Reasons for choosing test statistics are the same as

choosing the correct confidence interval formula

Note: It is difficult for us to find p-values for this test statistic because of the way our table is set up

Test Statistic

3

nsxt 0

STA 291 Spring 2010 Lecture 20

Results of confidence intervals and of two-sided significance tests are consistent◦ Whenever the hypothesized mean is not in the

confidence interval around the sample mean, then the p-value for testing H0: μ=μ0 is smaller than 5% (significance at the 5% level)

◦ In general, a 100(1-α)% confidence interval corresponds to a test at significance level α

Correlation Between Tests and Confidence Intervals

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Same process as with population mean Value we are testing against is called p0 Test statistic

P-value◦ Calculation is exactly the same as for the test for

a mean Sample size restrictions:

Significance Test for a Proportion

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STA 291 Spring 2010 Lecture 20

Let p denote the proportion of Floridians who think that government environmental regulations are too strict

A telephone poll of 824 people conducted in June 1995 revealed that 26.6% said regulations were too strict◦ Test H0: p=.5 at α=.05◦ Calculate the test statistic◦ Find the p-value and interpret

Construct a 95% confidence interval. What is the advantage of the confidence interval over the test

Example

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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

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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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