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STA 291 Fall 2009

STA 291 Fall 2009. Lecture 17 Dustin Lueker. Confidence Interval for µ. α =.02, n=16 t α /2 =. Sample Size.

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STA 291 Fall 2009

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  1. STA 291Fall 2009 Lecture 17 Dustin Lueker

  2. Confidence Interval for µ • α=.02, n=16 • tα/2= STA 291 Fall 2009 Lecture 17

  3. Sample Size • As with a confidence interval for the sample proportion, a desired sample size for a given margin of error (ME) and confidence level can be computed for a confidence interval about the sample mean • Found solving for ME in following confidence interval formula STA 291 Fall 2009 Lecture 17

  4. Confidence Interval for p • To calculate the confidence interval, we use the Central Limit Theorem (np and nq ≥ 5) • What if this isn’t satisfied? • Instead of the typical estimator, we will use • Then the formula for confidence interval becomes STA 291 Fall 2009 Lecture 17

  5. Comparison of Two Groups • Two independent samples • Different subjects in the different samples • Two subpopulations • Ex: Male/Female • The two samples constitute independent samples from two subpopulations • Two dependent samples • Natural matching between an observation in one sample and an observation in the other sample • Ex: Two measurements of the same subject • Left/right hand • Performance before/after training • Important: Data sets with dependent samples require different statistical methods than data sets with independent samples STA 291 Fall 2009 Lecture 17

  6. Confidence Interval for the Difference of Two Means • Take independent samples from both groups • Sample sizes are denoted by n1 and n2 • To use the large sample approach both samples should be greater than 30 • Subscript notation is same for sample means STA 291 Fall 2009 Lecture 17

  7. Example • In the 1982 General Social Survey, 350 subjects reported the time spend every day watching television. The sample yielded a mean of 4.1 and a standard deviation of 3.3. • In the 1994 survey, 1965 subjects yielded a sample mean of 2.8 hours with a standard deviation of 2. • Construct a 95% confidence interval for the difference between the means in 1982 and 1994. • Is it plausible that the mean was the same in both years? STA 291 Fall 2009 Lecture 17

  8. Comparing Two Proportions • For large samples • For this we will consider a large sample to be those with at least five observations for each choice (success, failure) • All we will deal with in this class • Large sample confidence interval for p1-p2 STA 291 Fall 2009 Lecture 17

  9. When would this be useful? • Is the proportion who favor national health insurance different for Democrats and Republicans? • Democrats and Republicans would be your two samples • Yes and No would be your responses, how you’d find your proportions • Is the proportion of people who experience pain different for the two treatment groups? • Those taking the drug and placebo would be your two samples • Could also have them take different drugs • No pain or pain would be your responses, how you’d find your proportions STA 291 Fall 2009 Lecture 17

  10. Example • Two year Italian study on the effect of condoms on the spread of HIV • Heterosexual couples where one partner was infected with HIV virus • 171 couples who always used condoms, 3 partners became infected with HIV • 55 couples who did not always use a condom, 8 partners became infected with HIV • Estimate the infection rates for the two groups • Construct a 95% confidence interval to compare them • What can you conclude about the effect of condom use on being infected with HIV from the confidence interval? • Was your Sex Ed teacher lying to you? STA 291 Fall 2009 Lecture 17

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