Question

A Campaign manager for a local politician is interested in the percentage of Leon County residents who intend to vote in the 2020 elections in November. Residents from each neighborhood in Leon County are randomly sample techniques, larger neighborhoods have a larger number of residents randomly sampled and smaller neighborhoods have a smaller number of residents randomly sampled to get a representative sample. Altogether 434 Leon County Residents are sampled. The result is that 39% of the sampled Leon County Residents intend to vote in 2020 elections in November.

(1)Suppose that someone at a local news station wants to consider the sampling variability and uses the results of the survey to calculate the margin or error for the result. The person at the station assumes that the normal distribution can be used in calculating the margin of error. Is the assumption of the normal distribution here correct?

A)Although a random sample was taken, the normal distribution is not appropriate since not enough residents were sampled

B)The normal distribution is appropriate since a random sample was taken and there were enough residents who answered "YES" as well as "NO" to voting in the 2018 midterms in November.

C) The normal distribution is not appropriate since only a sample of all the residents of Leon County were surveyed.

D)The normal distribution is appropriate since a random sample was taken and there were more than 30 residents surveyed.

(2)In the midterm primaries in August 2018, 37% of Leon County residents voted. Based on the information provided above, would it be surprising if 37% of all Leon County residents also intended to vote in the 2020 elections?

State Yes, or No and use statistical reasoning to support your position.

(3) Using the information from the sample above, what is your conclusion regarding the proportion of Leon County residents who intend to vote in the 2020 election in November?

Answer 1

Result:

A Campaign manager for a local politician is interested in the percentage of Leon County residents who intend to vote in the 2020 elections in November. Residents from each neighborhood in Leon County are randomly sample techniques, larger neighborhoods have a larger number of residents randomly sampled and smaller neighborhoods have a smaller number of residents randomly sampled to get a representative sample. Altogether 434 Leon County Residents are sampled. The result is that 39% of the sampled Leon County Residents intend to vote in 2020 elections in November.

(1)Suppose that someone at a local news station wants to consider the sampling variability and uses the results of the survey to calculate the margin or error for the result. The person at the station assumes that the normal distribution can be used in calculating the margin of error. Is the assumption of the normal distribution here correct?

B)The normal distribution is appropriate since a random sample was taken and there were enough residents who answered "YES" as well as "NO" to voting in the 2018 midterms in November.

(2)In the midterm primaries in August 2018, 37% of Leon County residents voted. Based on the information provided above, would it be surprising if 37% of all Leon County residents also intended to vote in the 2020 elections?

State Yes, or No and use statistical reasoning to support your position.

95% Confidence interval is (0.3441, 0.4359) which contains 37%. It is not surprising if 37% of all Leon County residents also intended to vote in the 2020 elections.

Correct option : No

Hypothesis test for proportion vs hypothesized value
	Observed	Hypothesized
	0.39	0.37	p (as decimal)
	169/434	161/434	p (as fraction)
	169.26	160.58	X
	434	434	n
		0.0232	std. error
		0.86	z
		.3881	p-value (two-tailed)
		0.3441	confidence interval 95.% lower
		0.4359	confidence interval 95.% upper
		0.0459	margin of error

(3) Using the information from the sample above, what is your conclusion regarding the proportion of Leon County residents who intend to vote in the 2020 election in November?

We conclude that proportion of Leon County residents who intend to vote in the 2020 election in November is not different from 37%.