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# Statistics Project: One-sample Hypothesis Testing For Proportions (Statistics Project Sample)

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one sample hypothesis testing

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One-Sample Hypothesis Testing
Students Name
University Name
One-Sample Hypothesis Testing
Hypothesis testing is employed in various field when we want to determine the validity of a certain claim made. The state of no change of the claim is placed on the null hypothesis whereas the claim is placed within the research/alternative hypothesis. In our case we will focus on a one-sample hypothesis test for proportions which is usually done on one sample. Data on election results will be employed here. Analysis will be done and results interpreted. The decision and conclusions made are based on the level of significance defined within the study. In our case, we will focus on the results garnered for George W Bush and find the proportion of the votes that he has earned from the votes. The votes for George W. Bush is 407. This gives us a proportion of 0.532.
From the case study, we have,
Sample size=765
Al Gore=358
George W. Bush=407
Level of significance (α) =0.10
The hypotheses for this case will be based on the claim made. That is, the network predicts the candidate as a winner if he wins more than 50% of the votes. Therefore, the hypothesized null hypothesis will be that the proportion is 50%. Hence proportion will be 0.50. This will be a right sided tests since we want to find out if the winner wins more than 50% of the votes. The hypotheses will be:
H0: p=0.50
Ha: p>0.50 (claim)
The results of this analysis are performed using excel and are as follows:
Z Test of Hypothesis for the Proportion
Data
Null Hypothesis =
0.5
Level of Significance
0.1
Number of Items of Interest
407
Sample Size
765
Intermediate Calculations
Sample Proportion
0.532026144
Standard Error
0.0181
Z Test Statistic
1.7716
Upper-Tail Test
Upper Critical Value
1.2816
p-Value
0.0382
Reject the null hypothesis
The decision will be to reject the null hypothesis if p-value<0.10 and make conclusions. From the above results, we can see that p-value=0.0382 which is less than 0.10 level of significance (α). Therefore, we will reject the null hypothesis and conclude that there is sufficient evidence to support the claim at 0.10 level of significance (α) and conclude that the networks should announce at 8:01 P.M. the Republican candidate George W. Bush will win the state.
We will change level of significance (α) to be 0.05 and find out if the same conclusions will be made. The results are as follows:
Z Test of Hypothesis for the Proportion
Data
Null Hypothesis =
0.5
Level of Significance
0.05
Number of Items of Interest
407
Sample Size
765
Intermediate Calculations
Sample Proportion
0.532026144
Standard Error
0.0181
Z Test Statistic
1.7716
Upper-Tail Test
Upper Critical Value
1.6449
p-Value
0.0382
Reject the null hypothesis
The decision will be to reject the null hypothesis if p-value<0.05 and make conclusions. From the above results, we can see that p-value=0.0382 which is less than 0.05 level of significance (α). Therefore, we will reject the null hypothesis and conclude that there is sufficient evidence to support the claim at 0.05 level of significance (α) and conclude that the networks should announce at 8:01 P.M. the Republican candidate George W. Bush will win the state.
We will change level of significance (α) to be 0.01 and find out if the same conclusions will be made. The results are as follows:
Z Test of Hypothesis for the Proportion
...

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