Introduction to Statistics – Test 4 Show working What a…
Introduction to Statistics – Test 4 Show working What are the possible forms of the alternative hypothesis in a hypothesis test? In hypothesis testing, what is: a) A type 1 error ? b) A type 2 error ? a) What does a p-value represent in a hypothesis test ? b) Is the null hypothesis ever proven to be true in a hypothesis test? Explain. It is thought that the mean length of trout in lakes in a certain region is 20 inches. A sample of 46 trout from one particular lake had a sample mean of 17.5 inches and a sample standard deviation of 4 inches. Conduct a hypothesis test at the 0.05 significance level to see if the average trout length in this lake is less than mu=20 inches. Use a p-value approach. Athletes at UC Boulder have a long term graduation rate of 69%. Recently, a sample of 34 athletes showed 20 graduates. Does this indicate that the population proportion of athletes who graduate is now less than 69%. Use a significance level of alpha=0.05. Use a critical region approach. Explain how your answer to question 4 would change if the population standard deviation of trout length was 4 inches instead of the sample standard deviation being 4 inches. If a confidence interval for the difference in two proportions contains some negative values and some positive values, what conclusion can you draw about the two proportions? Explain. In a clinical trail, 227 people were given OxyContin and 52 developed nausea. In that trial 45 people were given a placebo and 5 developed nausea. Use a 0.05 level significance for testing a difference in proportions of those who developed nausea when taking OxyContin versus a placebo. Hint….use a two-sided hypothesis test. Repeat question 8, only this time answer the question by constructing an appropriate confidence interval for the difference in proportions. 36 cans of regular coke had an average volume (xbar ) of 12.19oz and a sample standard deviation ( s ) of 0.11oz . 36 cans of pepsi had an average volume of 12.29oz and a sample standard deviation of 0.09oz . Use a 0.05 significance level to test the claim that cans of regular coke and regular pepsi have the same mean volume. Repeat question 10 by constructing an appropriate confidence interval for the difference in means. Considering the following data: Subject A B C D E Before 6.6 6.5 9.0 10.3 11.3 After 6.8 2.4 7.4 8.5 8.1 Use a dependent samples hypothesis test to test whether there is a significant difference between the Before and After levels. Helpful hint….the standard deviation of the differences in the 5 pairs of measurements is 1.646 ( I saved you needing to make that calculation ). Use a 0.01 level of significance ( alpha ). Construct a 95% confidence interval for the mean of the “Before/After” differences.
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