Ma 31100 Statistics

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Task 1: Solve the following problems: * A student of the author surveyed her friends and found that among 20 males, 4 smoke and among 30 female friends, 6 smoke. Give two reasons why these results should not be used for a hypothesis test of the claim that the proportions of male smokers and female smokers are equal. * Understand that this is not considered a random sample, but, a convenience sample. So you could not get the results that you would get from a random sample. * When setting up the formula you get np = x = 4 < 5, so the normal distribution cannot be used to get the approximate of binomial distribution * Given a simple random sample of men and a simple random sample of women, we want to use a 0.05 significance level to test the claim that the percentage of men who smoke is equal to the percentage of women who smoke. One approach is to use the P-value method of hypothesis testing: a second approach is to use the traditional method of hypothesis testing: and a third approach is to base the conclusion on the 95% confidence interval estimate of p1-p2. Will all three approaches always result in the same conclusion? Explain * The results will nearly always be the same as long as a confidence interval can be used. With using (a = .05) and a percent confidence (1 - .05 = 95%). This will happen between traditional approach and confidence interval approach. * Using the p-value approach and the confidence interval approach it will nearly be the same. Due to the standard error formula for p~1 – p~2 are slightly different for the CI approach the hypothesis testing approach. * For the results between the traditional and p-value approaches will always be the same, whether it is two tailed or not. Task 2: solace the following problems: * The mean tar content of a simple random sample of 25 unfiltered king size cigarettes is 21.1

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