One Sample Hypothesis – UOP
Based on the given scenario of election results in which the exit poll from the Florida state was conducted and the two main candidates were there from the Democratic Party and Republican Party. The member from the Democratic Party was Al Gore and from the Republican Party was George W. Bush. The research was conducted based on the voters’ sample of 765, out of which 358 casted votes for Democratic Party candidate Al Gore and 407 casted votes for Republican Party candidate George W. Bush. We all know that during the elections, the television networks cancel the routine programs just to provide the coverage related to the elections. It was expected that the polls will close at 8:00 p.m. The purpose of the television network was to know if the announcement should be made for the winner of the Republican candidate George W Bush at 8:01 p.m. The significance level for the analysis of one sample hypothesis test is given as 0.10.
The hypothesis testing includesthe null hypothesis and alternative hypothesis.Null hypothesis means there is no significant difference between the two values or means, on the other hand, the alternate hypothesis means there is a significant difference between the two values and means. Since we will conduct one sample hypothesis, the alternate hypothesis will represent either more than or less than sign. (Hypothesis Testing, n.d.)
Here, the null hypothesis means there is no clarity of the winning of Republican candidate George W. Bush, so announcement cannot be made at the television network for the win. It is represented as H0. The alternate hypothesis means there is clarity of the winning of Republican candidate George W. Bush, so the announcement can be made at the television network for the win. It is represented as H1 or HA. (Hypothesis Testing, n.d.)
Null hypothesis (H0) is p = 0.50
Alternate hypothesis (H1) is p > 0.50
Winning results can be declared if one out of the two members of election gets more than 50% votes. The voter sample size collected was 765. Since the sample size is more than 30 units, the most appropriate test is the Z test. The tabulated value of the Z test at 10% level of significance is 1.28. If the tabulated value is more than the calculated value then we will accept the null hypothesis and if the tabulated value is less than the calculated value then we will reject the null hypothesis. (Black, 2017) The z test formula applicable to the given situation is:
= ((x/n) – p0) / sqrt ((p0*(1-p0)) / n)
Total sample size (n) = 765
Number of votes for the winning candidate George W. Bush (x) = 407
Winning on the basis of getting more than 50% votes (p0) = 50/100 = 0.5
Insert all the values in the formula, we will get
z test= ((407/765) – 0.5) / sqrt ((0.5*(1- 0.5)) / 765)
= (0.532 – 0.5) / sqrt ((0.5*0.5) / 765) [divide 407 and 765 we get 0.532, subtract 1 and 0.5 we get 0.5]
= 0.032 / sqrt (0.25/765) [subtract 0.532 and 0.5 we get 0.032, multiply 0.5 and 0.5 we get 0.25]
= 0.032 / sqrt (0.000326) [divide 0.25 and 765 we get 0.000326]
= 0.032 / 0.018[Square root 0.000326, we get 0.018]
= 1.77 [divide 0.032 and 0.018, we get 1.77]
Summary of results
The results show the Z test value to be 1.77. The calculated value (1.77) is more than the tabulated value (1.28) which means the null hypothesis will be rejected and the alternate hypothesis will beaccepted. (Hypothesis Testing, n.d.) It can be stated that elections will be won by Republican candidateGeorge W Bush with more than 50% votes. (Black, 2017)Hence, the network should make an announcement for the winning of the candidate from the Republican Party at 8:01 pm.
Therefore, the analysis shows acceptance of alternate hypothesis which means Republican Party candidate George W. Bush will win the election by having more than the 50% votes and Democratic Party candidate Al Gore will get less than 50% votes. The network should make an announcement regarding the win of the Republican candidate George W. Bushat 8:01 p.m.
Black, K. (2017). Business Statistics: For Contemporary Decision Making (9th Edition). Hoboken, NJ, John Wiley & Sons. https://phoenix.vitalsource.com/books/9781119320890/epubcfi/6/18[;vnd.vst.idref=c01]!/4/2/2/2/6@0:0
Hypothesis Testing. (n.d.). http://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_hypothesistest-means-proportions/bs704_hypothesistest-means-proportions3.html