Inferential Statistics: Hypothesis Testing in Election Polls & Plans

This case study solution demonstrates the application of statistical hypothesis testing in two distinct scenarios: analyzing election polls and evaluating the effectiveness of a proposed payment plan. The first case uses a one-sample t-test to determine if there was a significant difference in voter preferences between Republican and Democrat candidates during the 2000 US election, concluding whether a network could confidently announce a winner based on exit polls. The second case employs a one-sample z-test to assess whether including stamped self-addressed envelopes in payment requests would significantly reduce the payment response time. Excel statistical tools were utilized to calculate the inferential statistics, leading to a recommendation to implement the proposed plan based on the potential for increased profitability due to faster payment cycles. The analysis supports the use of statistical tests for informed decision-making in business and real-world applications.

Case study scenarios
Introduction
Statistical tests are worthwhile in life in confirming the already existing belief as stated in the
alternative hypothesis. The aim of carrying out the statistical tests have been with the aim of
rejecting the null hypothesis Curtis, Bond, Spina, Ahluwalia, Alexander, Giembycz & Lawrence,
(2015). Various statistical tests exist but the choice of what to use depends on the number of
elements in a sample and what is to be tested Shamseer, Moher, Clarke, Ghersi, Liberati,
Petticrew & Stewart, (2015). In practical activities like in the scenarios provided for the
determination of the winner in the 2000 US polls between the republican and democrat
candidates and the determination the profitability of the plans in the organizations calls for
statistical hypothesis test input. The inferential statistics that will be used in the two scenarios
will be one sample t-test and one sample z-test in drawing the conclusion and making informed
decisions that will benefit the business.
Case 1 hypothesis testing
H0: Republican and democrat candidates had same chances of winning the 2000 states election
H1: Republican and democrats candidates had no same chances of winning 2000 states elections

t-Test: One-Sample
Votes
Mean 382.5
Variance 1200.5
Observations 2
Hypothesized Mean 0
df 1
t Stat 15.61224
P(T<=t) one-tail 0.020361
t Critical one-tail 3.077684
P(T<=t) two-tail 0.040721
t Critical two-tail 6.313752
Critical value at α = 0.10
Reject null hypothesis H0 if t>3.077684
Test statistic
t = 15.61224
p-value
p-value = 0.020361
Decision
Since t = 15.61224 > 3.078 we reject the null hypothesis that the Republican and democrat
candidates had same chances of winning the 2000 states election and conclude that basing on the
sample exit polls conducted in state of Florida taking a sample of 765 voters, there were enough
evidence to support the claim that the Republican and Democrats candidates had no same
chances of winning 2000 states elections. As a result therefore, if the polls were what to go by,
the network would announce the Republican candidate the winner immediately after the closure
of the polls stations (i.e. 8:01 PM).
Case 2 hypothesis testing
H0: μ => 24
H1: μ < 24

z-Test: One Sample for Means
Payment
Mean 21.63182
Known Variance 36
Observations 220
Hypothesized Mean 24
z -5.8543
P(Z<=z) one-tail 2.4E-09
z Critical one-tail 1.281552
P(Z<=z) two-tail 4.79E-09
z Critical two-tail 1.644854
Critical value at α = 0.10
Reject the null hypothesis if z< -1.645 or z > 1.645
Test statistic
z = -5.8543
P-value
p-value = 4.79E-09
Decision
Since z = -5.8543 which falls in the rejection region (i.e. -1.645 or 1.645) we reject the null
hypothesis i.e. μ => 24 and head further to conclude that there were enough evidence to conclude
that the proposed plan by the Chief Financial Officer to include stamped self-addressed envelope
would decrease the amount of time to less than 24 days. The initial amount of time was much
and the raising of the idea by the chief financial officer to improve on the appearance of the
envelopes by stamping self-address would have positive effects on time taken.
Conclusion
In conclusion, Excel statistical tools were used in the calculation of the inferential statistics i.e. t
and z values and the results were in the tables above. In the case study 1, determination of the

who to be announced at the end of polls, one sample t-test inferential statistic was used in testing
the hypothesis where from the results, the announcement of republican candidate George W.
Bush in the 2000 election at 8:01 PM would be appropriate and it therefore could be inferred that
the leading candidate (republican candidate) would amass enough votes to win the elections
since the test has confirmed that.
In case 2, Z-test was used being that the mean and standard deviation of time taken for response
by the clients was known. It could then be concluded that the chief financial officer’s idea of
including stamped addressed envelops would have the significant effect in reducing the number
of days as compared to the previous days. Since time was a factor and focus was in its reduction,
the applied statistical techniques in the test showed that if the plan of including self-addressed
envelope was implemented, the time for which payment was to be made would be decreased and
resulting to more profits to the company unlike when payment time was delayed. In response to
that therefore, the plan is firmly supported and advised to be implemented for the financial
benefits and profitability of the company.

References
Curtis, M. J., Bond, R. A., Spina, D., Ahluwalia, A., Alexander, S., Giembycz, M. A., ... &
Lawrence, A. J. (2015). Experimental design and analysis and their reporting: new
guidance for publication in BJP. British journal of pharmacology, 172(14), 3461-3471.
Shamseer, L., Moher, D., Clarke, M., Ghersi, D., Liberati, A., Petticrew, M., ... & Stewart, L. A.
(2015). Preferred reporting items for systematic review and meta-analysis protocols
(PRISMA-P) 2015: elaboration and explanation. Bmj, 349, g7647.