When an election for political office takes place, the television
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.
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Get Help Now!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 Al Gore and Republican George W. Bush. In a
sample of 765 voters, the number of votes cast for Al Gore was 358 and the
number of votes cast for George W. 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
George W. Bush will win the state. Use 0.10 as the significance level (α).
Case Study –
SpeedX
SpeedX, 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 have an MBA
from the University of Phoenix, and work for SpeedX as a business analyst. One
of your job duties is 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 in the Statistics course. 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 you gained in the class, 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
(α).
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