Consider the following hypothesis test: H0: pi S 12 Ha: p > 12 A sample of 25 provided a sample mean 5 = 14 and a sample standard deviation S = 4.32. a. Compute the value of the test statistic (to 2 decimals). b. Use the 15 distribution table (Table 2 in Appendix B) to compute a range for the p-value. The p-Value is - Select your answer - V c. At a = 0.05, what is your conclusion? - Select your answer - v . d. What is the rejection rule using the critical value? (Use CE = 0.05.) Reject H0 if t is the critical value of (to 3 decimals). Can you conclude that the population mean is greater than 12? - Select your answer - V Joan's Nursery specializes in customdesigned landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost estimating purposes, managers use two hours of labor time for the planting of a medium-sized tree. Actual times from a sample of 10 plantings during the past month follow (times in hours). 3.5 2.3 2.6 1.8 2.4 1.4 3.0 2.4 2.8 1.5 With a 0.05 level of significance, test to see whether the mean tree-planting time differs from two hours. a. State the null and alternative hypotheses. H0 :p, -Se|ectyouranswer- v 2 .Ha : p, -Se|ectyouranswer- v 2 b. Compute the sample mean. (to 2 decimals) c. Compute the sample standard deviation. (to 4 decimals) d. Find the test statistic and p-value. (Use Table 2 in Appendix B.) t (to 3 decimals) p-Value - Select your answer - V e. What is your conclusion? We reject the null hypothesis. There enough evidence to prove that the mean tree-planting time differs from 2 hours. According to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1,090 in 2018. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). a. A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of Ho will support the researcher's contention. Ho: M is - Select your answer - Ha: M is - Select your answer - b. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $920. Based on prior experience a population standard deviation of o = $1,800 may be assumed. What is the p-value (to 4 decimals)? c. Using a = 0.05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers? - Select your answer - d. Repeat the preceding hypothesis test using the critical value approach. Using a = 0.05, what is the critical value for the test statistic (to 3 decimals)? Enter negative value as negative number. State the rejection rule: Reject Ho if z is - Select your answer - the critical value. Using the critical value approach, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers? - Select your answer - vAccording to the IRS, taxpayers calling the IRS in 2017 waited 13 minutes on average for an IRS telephone assister to answer. Do callers who use the IRS help line early in the day have a shorter wait? Suppose a sample of 50 callers who placed their calls to the IRS in the first 30 minutes that the line is open during the day have a mean waiting time of 11 minutes before an IRS telephone assister answers. Based on data from past years, you decide that it is reasonable to assume that the standard deviation of waiting times is 9 minutes. Using these sample results, can you conclude that the waiting time for calls placed during the first 30 minutes the IRS help line is open each day is significantly less than the overall mean waiting time of 13 minutes? Use a = 0.05. State the hypotheses. H0: [A greater than or equal to 13 v Q9 Ha: M less than 13 v M What is the p-value (to 4 decimals)? 0.0384 0 Can you conclude that callers who use the IRS help-line early in the day have a shorter wait? No VM Last year, 44% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 35% planned to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 80 business owners. a. How many business owners in the survey planned to provide a holiday gift to their employees this year? Round your answer to the nearest whole number. b. Suppose the business owners in the sample do as they plan. Conduct a hypothesis test that can be used to determine whether the proportion of business owners providing holiday gifts had decreased from last year. State the hypotheses. H. =_0.44 H. =_0.44 Compute the test statistic and p-value. z-value (to 2 decimals) p-value (to 4 decimals) c. Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts decreased? Ho. We conclude that the proportion of business owners providing gifts has decreased from last year to this year. What is the smallest level of significance for which you could draw such a conclusion? (to 4 decimals)