One sample hypothesis testing cases qnt 561

Case Study – Election Results
Media platforms are important in that they help in shading light to people on any political elections being held. Exit polls are widely used by news media venues to conduct random sampling methods of data collection on the voters, whereby voters exiting the polling booths are asked on their opinions on their main preferred candidates whom they have voted for. It is from this information provided by the voters that a hypothesis test arises in order to determine whether the information given by the voters might provide clues on whom is expected to emerge as the winner in the voting process. (Black,2017). For this paper, will use the information on the elections held in the year 2000 between Democrat Al Gore and Republican George W. Bush. The voting process of this candidates would help us conduct a one-sample hypothesis in order to test and determine if the networks should announce at 8:01 P.M Republican candidate George W. Bush being the overall winner. Using 0.10 as the significance level (α). The polls close at 8:00 P.M. In a sample of 765 voters, 358 voters casted their votes to Al Gore while George W. Bush received 407 votes. Overall, the network gives the name of the possible winner if one of the candidates wins more than 50% of the votes.

The calculations to this is as follows:

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

normally the test statistic is distributed; thus, easy to determine the p-value as shown below:

Conclusion

In summary, due to the p-value being less than.10 it basically means that the result has fallen below the rejection region. The graph below helps in showing the manner in which the results have fallen in the rejection region as follows:

In addition, the results draw us to the hypothesis that George W. Bush possibly is going to get more than 50% of the total votes casted thus the announcements should be made by the network.

Case Study – Speed X
Speed X happens to be one of the largest courier company in the world today, its operations include a number of activities such as: reaching out to their customers by sending ready-made invoices as a way to request for payment from them within a span of 30 days. The invoices comprise of the specific addresses of this customers, customers are expected to use their received customized envelopes to make the expected payments. Mean and standard deviation are 24 days and 6 days respectively of the time taken by these customers to respond and pay their bills as required. The chief financial officer (CFO) has seen the need to have a self-addressed and stamped envelope representing the company as a way to help the company in improving its cash flow as a way to cover up the costs of stamps and envelopes as a result of decrease in the payment period by 2 days. (Black,2017) I selected randomly 220 customers where i decided to use the customized self-addressed and stamped envelopes with their respective invoices in order to determine how long the payment would take by their respective customers receiving the envelopes. The final information I received, helped me in conducting a one sample hypothesis test on the business in order to determine any possibilities of convincing the CFO to implement the plan as it would be of great importance and generate a lot of profits using a 0.10 and the significance level (α) as follows:

Null Hypothesis H0: µ = 30

Alternate hypothesis H1: µ < 30

Left-tailed test for single population mean

we can use z-test for hypothesis testing when the sample size is greater than 30.

At α = 0.10:

Descriptive statistics

Payment

Count

220

Mean

21.63

sample standard deviation

5.84

sample variance

34.05

minimum

9

maximum

39

Range

30

population variance

33.90

population standard deviation

5.82

standard error of the mean

0.39

confidence interval 90.% lower

20.98

confidence interval 90.% upper

22.28

margin of error

0.65

z

1.645

skewness

0.32

kurtosis

-0.23

coefficient of variation (CV)

26.98%

Conclusion

In conclusion, the information here shows no enough evidence to help in determining whether sending customized stamped envelopes or self-addressed envelopes helps in decreasing the payment duration by 2 days thus, at .10 significance level the null would not be rejected as follows:

In addition, the rejection region is the area left to the critical value -1.282. The shaded part is the rejection region thus the calculated test statistic does not fall under the shaded region.

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

e

n

s

i

t

y

1.282

0.1

0

1.772