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There are two cases studies, that we must solve using the
one-sample hypothesis to decide which will be the best decision. The first case
is the Election Result, that we will be using the a 0.10 as the significant
level (a).  As we will conduct a
one-sample hypothesis to test and determine if they will announce the winner of
the republican candidate George W. Bush after the poll closes at 8:00pm. The
second case is the Speed X and we will be using the a 0.10 and the significance
level = (a). However, the plan is to do the one-sample hypothesis test to
determine if we can convince the CFO to conclude the plan if it can be

Elections Results

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This election results of two candidates that have a chance
of winning which is the Democrat Al Gore and the Republican George W Bush, in the
exit poll having a sample of 765 voters. In the sample of 765, there was 358
voters who voted for Al Gore and 407 for George Bush. Now that we have the
sample and how many people voted, we can now see how the 0.10 significance
level and if Bush will win with more than 50% of voters. One candidate from the
election will win if they get over 50% of votes. So far, we can now apply to
test the proportion to test the hypothesis. The null and the alternate
hypothesis can be states as:

Null hypothesis: H0: P= 0.50

Alternate hypothesis: H1: P>

This is a right tailed test, due to be the right tailed one
sample test for the proportion the Z test was conducted using the a= 0.10. As
sample size is greater than 30, we can use the z-test to test the hypothesis, significance
level a= 0.10. Critical value at significance level 0.10 is calculated to be
1.28. The critical region is the area greater than the critical value of 1.28.

The decision is to test the
statistic that falls into the critical region, the null hypothesis will be

Z test statistic > Critical value = Z 0.10
= 1.28 this data was calculated by the Z test statistic=


test shows the result as the null being rejected at the 0.10 significance
level. Finally, from what the results showed the announcement will be given at
8:01pm announcing the Republican candidate George Bush the winner over the
Democratic Al Gore. George Bush had a higher percentage of voters making him win
the election for Florida.


Currently, the SpeedX case mean and standard deviation of
the amount of time taken by customers of to pay their bills are 24 days and 6
days respectively the latest has been 30 days. They have including a stamped
and self-addressed envelope with invoices, making an expectation to reduce
payment period by 2 days. We are going see if sending the envelope with stamped
and self-addressed will help with their invoices to reduces the payments period
from 24 days to 22 days. In this pilot study, a sample of 220 customers was
chosen, and self-addressed stamped envelopes were sent to the customers. We
have few numbers of days taken by customers that have paid the bill, and it was
recorded down. Based on this data and the excel spreadsheet, the hypothesis
test is to be conducted at 0.10 significance level to check if the payment
period has come down to 22 days. The null hypothesis and alternate hypothesis
are stated as:

Null Hypothesis H0: µ = 22

Alternate hypothesis H1: µ < 22 This is a left-tailed test for single population mean. As the population standard deviation is known so a Z-test for mean is the most appropriate test. This means, that the rejection area will be left to the critical value. As the Null hypothesis can be rejected if test statistic is less than the critical value. As sample size is greater than 30, we can use z-test for hypothesis testing; Considering a 0.10 significance level the rejection region is: Z test statistic < Critical value = -Z0.10 = -1.28 From the given data from the excel the Z test statistic = As we can see from the results the test statistic is not falling in the rejection region the null hypothesis should not be rejected at 0.10 significance level. However, the conclusion based on the result is that the data is not giving enough evidence that the plan would be profitable. But they have reduced the days of payments they receive.  

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