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

profitable.

Elections Results

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>

0.50,

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

rejected.

Z test statistic > Critical value = Z 0.10

= 1.28 this data was calculated by the Z test statistic=

.

The

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.

SpeedX

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.