Question

You want to estimate the percent of Democrats that will vote for Biden in the upcoming presidential election. You take a SRS of 50 Democrats and find that 42 of them plan to vote for Biden.

Answer the following: a) Determine the population(s) and parameter(s) being discussed. Remember, population is the group we are wondering about and parameter is a value that describes the whole group, like a mean. b) Determine which tool will help us find what we need (one sample z test, one sample t test, two sample t test, one proportion test, one sample z interval, one sample t interval, two sample t interval, one proportion interval) c) Check if the conditions for this tool hold. d) Whether or not the conditions hold, use the tool you chose in part (b). Use C=95% for all confidence intervals and α = 5% for all significance tests. ** Be sure that all methods end with a sentence describing the results. **

Answer 1

a) Population: The population comprises of all the Democrats in the States. The parameter of interest is the population proportion P of Democrats who will vote for Biden in the upcoming presidential election.

b) As we are interested in population proportion for one population, we can estimate the population proportion through the sample proportion. After this, a one proportion interval will help us find the significance of the estimate of population.

c) As the sample size is 50 (which is sufficiently large), the assumption for constructing the confidence interval, that the population is distributed normally can be taken to be true. The binary variable

X: Whether a Democrat votes for Biden or not

can be approximated to a normal distribution with mean and variance , where is the sample proportion of Democrats who will vote for Joe Biden.

Therefore, the population assumptions are satisfied.

d)

Therefore, we are 95% confident that the population proportion of Democrats who will vote for Joe Biden would lie in the interval (0.7384,0.9416).

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