Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 45% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners. (a) How many business owners in the survey plan to provide a holiday gift to their employees? 27 (b) Suppose the business owners in the sample do as they plan. Compute the p value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year. If required, round your answer to four decimal places. If your answer is zero, enter "0". Do not round your intermediate calculations. 0.4382 (c) Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts has decreased? We fail to reject cannot the null hypothesis. We conclude that the proportion of business owners providing gifts has decreased from 2008 to 2009. What is the smallest level of significance for which you could draw such a conclusion? If required, round your answer to four decimal places. If your answer is zero, enter "0". Do not round your intermediate calculations. The smallest level of significance for which we could draw this conclusion is ; because p-value greater than fail to reject the null hypothesis. a=0.05, we For the year 2010, 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,642. Assume that the standard deviation is σ = $2,280. If required, round your answer to two decimal places. (a) What are the sampling distributions of x for itemized deductions for this population of taxpayers for each of the following sample sizes: 30, 50, 100, and 400? = E(X) 16642 n σ(x) 30 $ 50 100 228.00 400 114.00 (b) What is the advantage of a larger sample size when attempting to estimate the population mean? A larger sample reduces standard error and results in a more population mean. the precise estimate of the

Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 45% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners. (a) How many business owners in the survey plan to provide a holiday gift to their employees? 27 (b) Suppose the business owners in the sample do as they plan. Compute the p value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year. If required, round your answer to four decimal places. If your answer is zero, enter "0". Do not round your intermediate calculations. 0.4382 (c) Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts has decreased? We fail to reject cannot the null hypothesis. We conclude that the proportion of business owners providing gifts has decreased from 2008 to 2009. What is the smallest level of significance for which you could draw such a conclusion? If required, round your answer to four decimal places. If your answer is zero, enter "0". Do not round your intermediate calculations. The smallest level of significance for which we could draw this conclusion is ; because p-value greater than fail to reject the null hypothesis. a=0.05, we For the year 2010, 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,642. Assume that the standard deviation is σ = $2,280. If required, round your answer to two decimal places. (a) What are the sampling distributions of x for itemized deductions for this population of taxpayers for each of the following sample sizes: 30, 50, 100, and 400? = E(X) 16642 n σ(x) 30 $ 50 100 228.00 400 114.00 (b) What is the advantage of a larger sample size when attempting to estimate the population mean? A larger sample reduces standard error and results in a more population mean. the precise estimate of the