There are two cases studies, that we must solve using theone-sample hypothesis to decide which will be the best decision. The first caseis the Election Result, that we will be using the a 0.10 as the significantlevel (a). As we will conduct aone-sample hypothesis to test and determine if they will announce the winner ofthe republican candidate George W. Bush after the poll closes at 8:00pm.
Thesecond case is the Speed X and we will be using the a 0.10 and the significancelevel = (a). However, the plan is to do the one-sample hypothesis test todetermine if we can convince the CFO to conclude the plan if it can beprofitable. Elections ResultsThis election results of two candidates that have a chanceof winning which is the Democrat Al Gore and the Republican George W Bush, in theexit poll having a sample of 765 voters. In the sample of 765, there was 358voters who voted for Al Gore and 407 for George Bush. Now that we have thesample and how many people voted, we can now see how the 0.
10 significancelevel and if Bush will win with more than 50% of voters. One candidate from theelection will win if they get over 50% of votes. So far, we can now apply totest the proportion to test the hypothesis. The null and the alternatehypothesis 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 onesample test for the proportion the Z test was conducted using the a= 0.10. Assample size is greater than 30, we can use the z-test to test the hypothesis, significancelevel a= 0.
10. Critical value at significance level 0.10 is calculated to be1.28.
The critical region is the area greater than the critical value of 1.28. The decision is to test thestatistic that falls into the critical region, the null hypothesis will berejected. Z test statistic > Critical value = Z 0.10= 1.
28 this data was calculated by the Z test statistic= . Thetest shows the result as the null being rejected at the 0.10 significancelevel. Finally, from what the results showed the announcement will be given at8:01pm announcing the Republican candidate George Bush the winner over theDemocratic Al Gore. George Bush had a higher percentage of voters making him winthe election for Florida. SpeedXCurrently, the SpeedX case mean and standard deviation ofthe amount of time taken by customers of to pay their bills are 24 days and 6days respectively the latest has been 30 days.
They have including a stampedand self-addressed envelope with invoices, making an expectation to reducepayment period by 2 days. We are going see if sending the envelope with stampedand self-addressed will help with their invoices to reduces the payments periodfrom 24 days to 22 days. In this pilot study, a sample of 220 customers waschosen, and self-addressed stamped envelopes were sent to the customers. Wehave few numbers of days taken by customers that have paid the bill, and it wasrecorded down.
Based on this data and the excel spreadsheet, the hypothesistest is to be conducted at 0.10 significance level to check if the paymentperiod has come down to 22 days. The null hypothesis and alternate hypothesisare stated as:· Null Hypothesis H0: µ = 22 · Alternate hypothesis H1: µ < 22This is a left-tailed test for single population mean. Asthe population standard deviation is known so a Z-test for mean is the mostappropriate test. This means, that the rejection area will be left to thecritical value.
As the Null hypothesis can be rejected if test statistic isless than the critical value. As sample size is greater than 30, we can usez-test for hypothesis testing; Considering a 0.10 significance level therejection region is:Z test statistic < Critical value = -Z0.10 = -1.28From the given data from the excelthe Z test statistic = As we can see from the results the test statistic is notfalling in the rejection region the null hypothesis should not be rejected at0.
10 significance level. However, the conclusion based on the result is that thedata is not giving enough evidence that the plan would be profitable. But theyhave reduced the days of payments they receive.