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Problem 1 Use the Old Faithful data labelled Duration as a sample for problem 1. a. Determine the proportion of instances that the duration was less than 240 seconds. Also express the proportion as a percent. (hint: proportion is number of successes divided by total number. b. Calculate the 95% confidence interval of the proportion. What is the margin of error? c. Calculate the 90% confidence interval of the proportion. d. For a 95% confidence level and a margin of error of 3% (0.03), how many samples are needed?
Problem 2 Use the Old Faithful data labelled Duration as a sample for problem 2. Test the assertion that the mean duration time of the geyser eruption is less than 240 seconds. (hint: this is a one-sample t test for testing a claim about a mean with sigma not known -- see chap.8-4) Be sure to state: a. The mean and standard deviation of the sample b. H0 and H1 c. The value of the statistic (t) calculated d. Probability value with your conclusion, using alpha=0.05
Problem 3 Use the HWAS data for problem 3. Assume HWAS data is a Population, and use the Gender column of the data set. Take a Simple Random Sample from the Gender column of n=30. Test if the proportion of the SRS data that is female equals 0.6. (hint: this is a one-sample proportion test for testing a claim about a proportion -- see chap.8-3) Be sure to state: a. How you did the sampling, and the proportion of the SRS that is female. b. H0 and H1 c. Using alpha=0.05, the value of the statistic (z) calculated d. Probability value with your conclusion, using alpha=0.05
Problem 4 Use the HWAS data for problem 4. Assume HWAS data is a Population, and use the Age column of the data set. Take a Simple Random Sample from the Age column of n=30. a. For this SRS of 30, find the Mean, Std.Deviation, Five-Number Summary, and identify Outliers. Make histogram, and describe distribution. Description should be in sentence form and should include min, max, outliers, shape of histogram, number of peaks, etc. b. Based on the SRS, calculate the best point estimate of the population mean Age ? c. To calculate a 95% confidence level of the sample mean, determine the critical t value and the sample std.deviation. Compute the margin of error and confidence interval. (hint: See chap.7-4 on estimating population mean with sigma not known.) d. How many are needed in a sample to achieve a margin of error of 3 years at 95% confidence level? e. Using the complete Age column of the HWAS data set (the Population), make a histogram and find the mean. Compare with SRS histogram and mean from part a. Does the Population mean Age fall within the confidence interval ? Explain why it is possible for the sample and the population to be dissimilar.
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