QNT week 5

Case Study – Election Results

Political elections tend to take over on news media venues. Exit polls are used wherein a random sample of voters who are exiting the polling booths are asked for whom they voted. It is from that data collected that a hypothesis test is applied to determine whether there is enough evidence to infer the leading candidate will acquire enough votes to win. For this paper, we will use the 2000 year elections with Democrat Al Gore and Republican George W. Bush to 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). The polls close at 8:00 P.M. 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 null hypothesis is H0: p = 0.50

Alternate hypothesis is H1: p > 0.50

Right tailed test means z test statistic =

Significance level α = 0.10.

The critical value at significance level 0.10 is calculated as 1.28

p0 = null hypothesis proportion = 0.5

x = George W. Bush 407

n = 765

Test statistic is calculated as: z = = 1.7716

The test statistic is normally distributed; therefore, we can determine the p-value it is:

Conclusion

In conclusion, because the p-value is less than .10 it has fallen below the rejection region. In the graph below you can see that the results fall in the rejection region. This means we accept the alternate hypothesis that George W. Bush will get more than 50% votes and the network should make the announcement.

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) wants to start including a stamped self-addressed envelope to improved cash flow from a 2-day decrease in the payment period and believes it would pay for the costs of the envelopes and stamps. As a business analyst for SpeedX, I have to run analytics and present the results to the senior management for critical decision-making. I decided to randomly select 220 customers and propose to include a stamped self-addressed envelope with their invoices and record the numbers of days until payment is received. With that information I will then conduct a one-sample hypothesis test and determine if you can convince the CFO to conclude that the plan will be profitable using a 0.10 and the significance level (α).

Null Hypothesis H0: µ = 30

Alternate hypothesis H1: µ < 30

Left-tailed test for single population mean

With a sample size greater than 30, we can use z-test for hypothesis testing.

At α = 0.10:

Conclusion

There is not enough evidence to show that sending stamped and self-addressed envelopes to customers reduces payment time by 2 days because the the null would not be rejected at .10 significance level.

References

Black, K. (2017). Business statistics for contemporary decision making (9th ed.). Hoboken, NJ: John Wiley & Sons, Inc.

0.4

0.3

0.2

0.1

0.0

Dashed line is the test statistic and shaded are is the critical region

D

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n

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y

1.282

0.1

0

1.772

Critical Region and the test statistic