Suppose that there are two (2) candidates (i.e., Jones and Johns) in the upcoming presidential election. Sara notes that she has discussed the presidential election candidates with 40 friends, and 27 said that they are voting for candidate Jones. Sara is therefore convinced that candidate Jones will win the election because Jones gets more than 50% of votes.
Answer the following questions in the space provided below:
⦁ Based on what you now know about statistical inference, is Sara’s conclusion a logical conclusion? Why or why not. What inference test should she use? On your own
In a hypothesis test, first we need to state our Null and Alternative hypothesis to test the statement. After, we can conclude our analysis based on the Hypothesis Test. In this problem, we use a Z-Hypothesis Test for a Population Proportion. Our Null Hypothesis is Ho<- 0.5 and our alternative hypothesis is H1>0.5. Since our alternative is a greater inequality symbol, we need to use a right tail hypotheses test.
2. What z-score did she obtain? On your own. Keep in mind that p hat is the proportion of the fraction of friends who answered Sara, and that Po is the probability of winning. In this case is stating 50% or 0.5; so, Po = 0.5
Use this formula:
⦁ What should her conclusion state?
Calculate P value: Already done for you:
P value is 0.027 <0.05 Reject the Null Hypothesis. The reason is that we use a 95% confidence interval, and this is a right tail hypothesis. Thus, we use an alpha of 5% error or 0.05. Once the p value is calculated by using 1-(p>- Zo); Zo is found on the Z table.
Below is a graphic explanation of P-value
⦁ Compute the 95% confidence interval? The Z value to calculate a 95% one tail is 1.645
Use the formula below to calculate the interval. I have done it for you, your interval should be approx. between (53% to 82%).
5. What role does the margin of error play in determining how many individuals should be sampled if we desired a margin of error plus or minus .000001? On your own
6. How would you explain your conclusion to Sara without using any statistical jargon? In other words, is her original sample size sufficient or should she interview more people to obtain an accurate prediction. On your own.