Step 1: Stating the hypotheses
The question is whether the networks should announce George W. Bush as the elections winner at 8:01pm having gained more than 50% of the votes cast. From the polls conducted, the null hypothesis is that George W. Bush will get votes less or equal to 50% against the alternative hypothesis that He will get more than 50% of the vote cast.
This can be statistically written as:
Where p is the proportion of people who voted for George W. Bush
Step 2: The significance level
The significance level given for this study is 0.1
Type I Error - Declare George Bush the winner when he wins less than or equal to 50% of the votes
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Type II Error - Declare Bush the winner when he wins less than 50% of the votes
The worst error the network could make is declaring George Bush the winner when he has not actually won. This could cause more humiliation to the networks and George Bush if the opposite would happen.
Step 3: Test Statistic
The test statistic required for this study is the p-statistic test
Calculation
p=407/765 =0.532
=
At 95% confidence level, the p-value is given by
P (N (0, 1) > 1.77 = 0.384
Step 4: Comparing the p- value above with a
From the above calculations it is clear that 0.384>0.05
Therefore, we fail to reject the null hypothesis that George W. Bush will get votes less or equal to 50% of the total votes cast.
Step 5: Conclusion
We can therefore conclude that by 8:01pm, the networks will not have declared George W. Bush as the winner.
Case 2: Speed X:
Step 1: Stating the Hypotheses
The question is whether the stamped self-addressed envelopes would decrease the amount of time taken to pay the bills.
Ho = Self-addressed envelope has a return rate greater than or equal to 22 days
H 1 = Self-addressed envelope has a return rate less than 22 days
This is statistically written as
Step 2: Significance level
The level of significance is given by 0.1
Type I error – Rejecting that self-addressed envelope has a return rate greater than or equal to 22days when it is indeed the case
Type II error – Retaining that the envelopes have a return rate of less than 22 days when it is false.
The worst case scenario would be for the company to commit type II error since it would lead to losses.
Step 3: find the p value
The data collected on the return days from 220 customers was as follows:
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, 31, 19, 27, 19, 26, 26, 26, 23, 12, 20, 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, 29, 28, 14, 21, 30, 19, 14, 31, 19, 14, 21, 28.
Form normal tables, the corresponding value for -0.914 is 0.1814 making it our p-value
An extract from Excel Worksheet
Step 4: comparing the p value with a
With a confidence level of 95%
It is clear that 0.184>0.05
We therefore reject the null hypotheses that the return rate is greater than or equal to 22 days
Step 5: Conclusion
In conclusion, we find out that the Chief Financial Officer was right to include stamps on the self-addressed envelopes. It was found out that the return rated is even less than 22 days as she had suggested. This would improve the cash flow and enable the business to cover the costs of envelopes and stamps.
References
Hinkle, D. E., Wiersma, W., & Jurs, S. G. (2003). Applied statistics for the behavioral sciences.
Moore, D. S. (2007). The basic practice of statistics (Vol. 2). New York: WH Freeman.
Mendenhall, W., Beaver, R. J., & Beaver, B. M. (2012). Introduction to probability and statistics . Cengage Learning.
Khazanie, R. (1984). Elementary Statistics, in a World of Applications . Scott Foresman.
