Chapter 8 Review Large Sample Small Sample Binomial Choosing Sample Size
• A random sample of 60 employees opf a large corporation had a sample mean x=32. 5 accumulated vacation days with sample standard deviation s=18. 5 days. Find a 90% confidence level for the population mean number of accumulated vacation days.
• A random sample of 50 calls initiated on cellular phones had a mean duration of 3. 5 minutes with standard deviation 1. 2 minutes. Find a 99% confidence interval for the population mean duration of telephone calls initiated on cellular phones.
• A random sample of ten jumbo burgers from a local diner had the following weights (in ounces. ) If µ is the mean weight of all jumbo burgers served at the diner, find a 99% confidence interval for µ. 12. 1 12. 4 11. 8 12. 6 11. 9 11. 5 12. 2 11. 3 11. 7 12. 3
• In wine making, acidity of the grape is a crucial factor. A p. H range from 3. 1 to 3. 6 is considered very acceptable. A random sample of 12 bunches of grapes was taken from a California vineyard. The sample mean acidity was 3. 38 with sample standard deviation 0. 20. Find a 99% confidence interval for the mean acidity of the entire harvest of grapes from this vineyard.
• A postmaster in a large city found that 56 packages out of a random sample of 400 packages had insufficient postage. Find a 99% confidence interval for the population proportion of packages with insufficient postage.
• A member of the House of Representatives wants to determine the proportion of voters in her district who favor a flat income tax. A random sample of 200 voters in her district showed 89 in favor. Let p represent the proportion of voters who favor a flat income tax. A) Find a point estimate for p B) Find a 95% confidence interval for p C) Does the data indicate whether a majority of the voters oppose the tax? Explain.
• A seed company advertises that the mean time from planting to harvest for a new variety of zucchini seeds is 50 days. The standard deviation is estimated to be 10. 3 days. If we wanted to verify this claim how large a sample would we need in order to state with 95% confidence that our sample mean differs from the population mean by no more than 3 days?
• Union officials want to estimate the percent, p, of workers in the Big Bend Metalworks who favor a strike. The union wants to have 90% confidence that its estimate for p is within 2. 5% of the true proportion of workers who favor a strike. A) If no accurate estimate for p is available, how large a sample of workers is necessary? B) A preliminary sample of 100 workers gave r/n=0. 35. How many more workers should be included in this sample?
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