Payment 27 24 14 39 13 31 26 33 13 23 17 24 18 34 13 23 16 32 30 29 21 19 22 14 27 20 11 20 30 24 18 21 24 18 27 27 27 21 22 23 18 17 23 26 20 20 22 21 13 36 18 25 26 19 16 28 16 20 16 14 25 14 35 17 16 19 19 17 18 22 23 22 27 23 23 21 20 18 29 32 27 15 21 26 32 20 29 25 15 21 30 24 23 14 18 22 37 24 35 29 24 17 27 15 19 12 19 21 19 21 15 17 20 21 31 19 27 19 26 26 26 23 12 20 34 21 24 20 21 16 23 13 19 18 31 29 23 28 19 19 22 24 21 23 14 25 17 22 21 18 22 15 27 14 23 25 24 24 17 16 30 24 17 27 24 17 10 25 15 13 29 21 22 11 25 30 23 18 19 18 14 21 22 17 19 23 31 26 25 15 16 28 27 22 12 25 12 21 19 26 16 21 30 16 25 13 11 13 22 28 14 21 30 19 14 31 9 14 21 28 Election Case When an election for political office takes place, tv networks cancel regular programming and instead, provide election coverage. When the ballots are counted, the results are reported. However, for important offices such as president or senator in large states, the networks actively compete to see which will be the first to predict a winner. This is done through exit polls, wherein a random sample of voters who exit the polling booth is asked for whom they voted. From the data, the sample proportion of voters supporting the candidates is computed. Hypothesis testing is applied to determine whether there is enough evidence to infer the leading candidate will garner enough votes to win. Suppose in the exit poll from the state of Florida during the 2000 year elections, the pollsters recorded only the votes of the two candidates who had any chance of winning: Democrat Gore and Republican Bush. In a sample of 765 voters, the number of votes cast for Gore was 358 and the number of votes cast for Bush was 407. The network predicts the candidate as a winner if he wins more than 50% of the votes. The polls close at 8:00 P.M. Based on the sample results, conduct a one-sample hypothesis test to determine if the networks should announce at 8:01 P.M. the Republican candidate Bush will win the state. Use 0.10 as the significance level (). Speed Case Speed, a large courier company, sends invoices to customers requesting payment within 30 days. The bill lists an address, and customers are expected to use their own envelopes to return their payments. Currently, the mean and standard deviation of the amount of time taken to pay bills are 24 days and 6 days, respectively. The chief financial officer (CFO) believes including a stamped self-addressed envelope would decrease the amount of time. She calculates the improved cash flow from a 2-day decrease in the payment period would pay for the costs of the envelopes and stamps. You will need to run analytics and present the results to the senior management for critical decision-making. You see this as an opportunity to utilize some of the skills you gained. Because of your strong understanding and background in inferential statistics, you decide to take up this important assignment. You have learned any analysis in inferential statistics starts with sampling. To test the CFO's belief, you decide to randomly select 220 customers and propose to include a stamped self-addressed envelope with their invoices. The CFO accepts your proposal and allows you to run a pilot study. You then record the numbers of days until payment is received. Using your statistical expertise and skills, conduct a one-sample hypothesis test and determine if you can convince the CFO to conclude that the plan will be profitable. Use 0.10 and the significance level ()