# Essay Example on Hypotheses Using Statistics

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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 and the Democrat candidate after the poll closes at 8 00pm The second case we are presenting is the SpeedX and we will be using the excel spreadsheet as well with the 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 will be stated as follow 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 The critical value at a significance level of 0 10 is calculated to be 1 28 Therefore the critical region has an 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 Z lim y_ 0 5x 1 0 5 u 5 σ 5 0 50 1 7716 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 a 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 of statistic comes out to be less than the critical value As the 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 21 6318 21 0 6 22 O 0 9102 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 my conclusion based on the result we just did and analyzed everything the data did not give us enough evidence that the plan would be profitable for them But they have reduced the days of payments they been receiving

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