In your own words, how are a one-sample z-test and one-sample chi-square test different? How would we decide which test is correct to use?

Math problems

FiveThirtyEight is a political polling organization that uses statistics to understand the world around us. They are interested in understanding how eligible voters will cast their ballot for the upcoming midterm elections. As a starting point, they want to know whether there is an equal number of voters that identify with the three types of political parties (i.e., Democrat, Independent, and Republican). Based on a series of polls conducted over the past two weeks with 10,000 individuals who are eligible and planning to vote, they found that 3,126 voters identified with Democrats, 4,124 identified with Independents, and 2,750 identified with Republicans.

Did FiveThirtyEight find an equal number of voters in the three types of political parties, or were some parties more popular than others? Use the conventional critical alpha value of .05. In your answer, you should report the chi-square value (χ2), the critical chi-square value that needs to be exceeded, and make a decision about the hypothesis.

Over the past three semesters, I asked students in my two classes (n = 132) about their vacation preferences. Excluding the category “Other”—which no one selected—there were six options to choose from: Mountains/wilderness, Beach, Cruise, Explore a new city, Road trip, and A trip abroad. The two most frequently selected options were “A trip abroad” (51 times) and “Beach” (45 times). “Explore a new city” (15 times), “Cruise” (8 times), “Mountains/wilderness” (7 times), and “Road trip” (6 times) were also selected.

Assuming that these vacations are equally preferred in the general population, do the preferences of students in my classes differ from the population? Use the conventional critical alpha value of .05. In your answer, you should report the chi-square value (χ2), the critical chi-square value that needs to be exceeded, and make a decision about the hypothesis.

SPSS problem

For this problem, you will need to download the datafile posted on Blackboard titled, “Class Survey F21_Vacation.sav”.

First, run a Frequency analysis on the variable “Vacation” and include a bar chart. Copy and paste (or take a screenshot) of the bar chart that SPSS produces.

Second, perform a one-sample chi-square test on the “Vacation” data. Copy and paste (or take a screenshot) of the output that SPSS produces.

Third, report your findings in APA format. This should include the chi-square value (χ2), degrees of freedom (df), p-value, and a decision about the hypothesis.