Expected counts in chi-squared tests with 2-way tables

Naina obtained a random sample of 225 American high school students and collected their responses to the following questions: "What is your gender?" and "What is your favorite season of the year?" Here are the results: Naina wants to perform a \chi^2χ2\chi, squared test of independence between gender and favorite season in this population. What is the expected count for the cell corresponding to female students whose favorite season is spring?

13.56

Maud and Billy wanted to know if there's a difference between the modes of transportation used by men and women. One morning, they stood at the entrance to a big office building and surveyed people about the mode of transportation they used to get to the office. Maud surveyed a random sample of 110 women and Billy surveyed a random sample of 110 men. Here are the results: They want to perform a \chi^2χ2\chi, squared test of homogeneity on these results. What is the expected count for the cell corresponding to women who walk?

14

Edison, Xiu, and Amia are childhood friends who go to different high schools. They were wondering if there's a difference between their schools in the number of friends people have on social media. They each surveyed a random sample of students from their schools, asking for the number of friends they have on social media. Here are the results: They want to perform a \chi^2χ2\chi, squared test of homogeneity on these results. What is the expected count for the cell corresponding to students from Edison's school that have more than 300 friends?

22.33

Margot surveyed a random sample of 180 people from the United States about their favorite sports to watch. Then she sent separate, similar, survey to a random sample of 180 people from the United Kingdom. Here are the results: Margot wants to perform a \chi^2χ2\chi, squared test of homogeneity on these results. What is the expected count for the cell corresponding to people from the United Kingdom whose favorite sports to watch is tennis?

27

A zoo has separate habitats for its three types of bears: brown, black, and grizzly bears. Each habitat offers three areas for the bears to spend their time: an outdoor area, an indoor area, and a pool. Gisele is the zookeeper who cares for the brown bear. She takes a random sample of 10 moments each day for a week and records which area the brown bear is at each of those moments. Bryan and Adele use a similar strategy and obtain separate samples of 70 observations for the black and grizzly bears, respectively. Here are their results: They want to perform a \chi^2χ2\chi, squared test for homogeneity to judge if the bears are spending their time differently in their habitats. What is the expected count for the cell corresponding to the grizzly bear being by the pool?

27.67

Liv collected information about the length and width of a random sample of 48 petals of iris flowers. Here are the results: Liv wants to perform a \chi^2χ2\chi, squared test of independence between petal length and width. What is the expected count for the cell corresponding to petals whose length is more than 5.7cm and whose width is more than 2cm?

7.67

Tate works at an ice cream stand. Every customer can choose one of two toppings—sprinkles or chocolate chips. He recorded the age group and the chosen topping for a random sample of 120120120 customers. Here are the results: Tate wants to perform a \chi^2χ2\chi, squared test of independence between age and topping. What is the expected count for the cell corresponding to adults that chose sprinkles?

16

Rashad is a hotel manager. He surveyed a random sample of 120 guests and asked them which floor their room was and about their level of satisfaction. Here are the results Rashad wants to perform a \chi^2χ2\chi, squared test of independence between floor and satisfaction. What is the expected count for the cell corresponding to satisfied guests that stayed in floors 7 to 9?

21.22

Judson collected information about the name length and the population of a random sample of 296 American cities. Here are the results: Judson wants to perform a \chi^2χ2\chi, squared test of independence between name length and population. What is the expected count for the cell corresponding to cities with more than 250,000 residents whose name has less than 8 characters?

33.45

A certain car model comes in four different colors (black, white, blue, and silver) and can either have automatic or manual transmission. The company that makes the car took a random sample of 384 cars that were sold and checked their color and transmission. Here are the results: The company wants to perform a \chi^2χ2\chi, squared test of independence between color and transmission. What is the expected count for the cell corresponding to a white car with manual transmission?

51

Mabel made a change to the website she runs, and she wonders how it affected the way people navigate to the website—from a web search, from social media, or directly by entering the website's address. She took a random sample of 170 visits before she made the change, and then she took a random sample of 170 visits after she made the change. Here are the results: Mabel wants to perform a \chi^2χ2\chi, squared test of homogeneity on these results. What is the expected count for the cell corresponding to navigation from social media before Mabel made the change?

64

A random sample of internet subscribers from the west coast of the United States was asked if they were satisfied with their internet speeds. A separate random sample of adults from the east coast was asked the same question. Here are the results: A market researcher wants to perform a \chi^2χ2\chi, squared test of homogeneity on these results. What is the expected count for the cell corresponding to east coast subscribers who responded "yes"?

19.2