Data was collected from a simple random sample of 200 cell phone users age 18 or older in the United States. Each user was categorized by age-group and by whether he or she uses a certain cell phone app. The table shown summarizes the data, with expected cell counts in parentheses.Uses Cell Phone AppAge-Group Yes No Total Young Adults 4(15.2)76(64.8)80 Older Adults 29(19.38)73(82.62)102 Elderly Adults 5(3.42)13(14.58)18 Total 38162200 Which statement is true about whether the conditions for a chi-square test for independence have been met?a. All necessary conditions are satisfied to apply a chi-square test for independence between age-group and texting use by cell phone users.b. The data from the different age-groups are not the result of independent random samples; therefore, the conditions for the test are not met.c. The total sample size in one or more of the age-groups is too small to meet the conditions of the chi-square test for independence.d. Not all of the observed cell counts are large enough to satisfy the conditions for the chi-square test for independence.e. Not all of the expected cell counts are large enough to satisfy the conditions for the chi-square test for independence.

Question

Data was collected from a simple random sample of 200 cell phone users age 18 or older in the United States. Each user was categorized by age-group and by whether he or she uses a certain cell phone app. The table shown summarizes the data, with expected cell counts in parentheses.Uses Cell Phone AppAge-Group Yes  No  Total  Young Adults 4(15.2)76(64.8)80 Older Adults 29(19.38)73(82.62)102 Elderly Adults 5(3.42)13(14.58)18 Total 38162200 Which statement is true about whether the conditions for a chi-square test for independence have been met?a. All necessary conditions are satisfied to apply a chi-square test for independence between age-group and texting use by cell phone users.b. The data from the different age-groups are not the result of independent random samples; therefore, the conditions for the test are not met.c. The total sample size in one or more of the age-groups is too small to meet the conditions of the chi-square test for independence.d. Not all of the observed cell counts are large enough to satisfy the conditions for the chi-square test for independence.e. Not all of the expected cell counts are large enough to satisfy the conditions for the chi-square test for independence.

Jazlyn Mitchell · Accepted Answer

Introduction:It is of interest to test if the age-group of a person and whether or not they use cell phone apps are independent of one another, using the chi-square test of independence.Explanation:The primary assumptions and conditions that must be satisfied in order to conduct a chi-square test of independence are as follows:1. The sample must be collected using random methods, to ensure that the observations are all independent of one another and there is no unnecessary bias.2. The variables of interest, the association between which is to be tested, must be categorical, each with at least two categories.3. The expected count for each cell representing a combination of the levels of the categorical variables of interest must be at least 5.Here, it is mentioned that the sample is collected using random methods. As a result, the observations are independent of one another.There are two variables of interest: “age group” of adults, and whether or not the adult “uses cell phone app”. Since the age group is classified into three levels- “young adults”, “older adults” and “elderly adults”, it is a categorical variable, with three levels. Again, the variable “uses cell phone app” has two levels- “yes” and “no”, which are two categories, and thus, “uses cell phone app” is also a categorical variable.However, the expected frequency for all the cells is not at least 5. It can be observed that the expected frequency for “elderly adults” whose response to “uses cell phone app” is “yes” is 3.42, given in parentheses.Thus, the first two conditions are met. However, the condition that “expected count for each cell must be at least 5” for a chi-square test of independence is not met.Thus, the correct answer is Option E.

Data was collected from a simple random sample

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