PSY230_M7_Assignment_Spring2024

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Arizona State University *

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230

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Statistics

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Feb 20, 2024

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Uploaded by EarlLightning13238

PSY230_Bienemann Spring 2024 M7 Assignment (30 Points) *Unlike prior assignments, you will NOT be submitting a Word document and Excel file. Instead, you will need to work through this assignment and provide your answers in the M7 Assignment (Special Quiz Format) quiz. I recommend filling out your answers on this sheet before taking the quiz and keeping it on hand for reference. You will have 2 attempts at the quiz, so if you get marked incorrect on an answer, you can go back through your work and try to correct any errors before taking the quiz the second time. Assignment Direction: Complete the Guided Practice Problem first, if you have not done so. It will help you become proficient in answering the questions in this assignment. Q1) Chi-Square Test for Goodness of Fit (7 points) Two employees at an ice cream store were discussing the popularity of four of the ice cream flavors they have: Vanilla, Chocolate, Mint, and Strawberry. Employee A thought that the four flavors are equally popular, but employee B didn’t think so. To settle their debate, they decided to tally the number of customers asking for those flavors for a whole day. There were 44 customers that day:  5 asked for vanilla  15 asked for chocolate  14 asked for Mint  10 asked for strawberry Conduct a Chi-Square Test for Goodness of Fit to answer the research question of whether the four flavors are equally popular, using  = .05 as the significance level. a. The variable under examination is the type of ice cream flavor, such as Vanilla, Chocolate, Mint, and Strawberry. This variable is of the nominal type, indicating categories or names without any inherent order or ranking. b. The null hypothesis (H0) states that all ice cream flavors are equally popular. The alternative hypothesis (H1) proposes that at least one flavor is more popular than the others. c. The calculated Chi-Square statistic is approximately 5.637. d. The degrees of freedom (df) are 3, and the critical value for a significance level of 0.05 is approximately 7.815. e. Since 5.637 < 7.815, we fail to reject the null hypothesis. f. Based on our analysis, we lack evidence to conclude that the flavors of ice cream are not equally popular among customers. Therefore, we cannot reject the null hypothesis. Q2) Chi-Square Test for Goodness of Fit (7 points) All course content and materials, including this assignment and all other items published within the Canvas course shell, are copyrighted materials and students may not share outside the class, upload to online websites not approved by the instructor, sell, or distribute course content or notes taken during the conduct of the course (see ACD 304–06 , “Commercial Note Taking Services” and ABOR Policy 5-308 F.14 for more information). Students must refrain from uploading to any course shell, discussion board, or website used by the course instructor or other course forum, material that is not the student’s original work, unless the students first comply with all applicable copyright laws; faculty members reserve the right to delete materials on the grounds of suspected copyright infringement.

PSY230_Bienemann Spring 2024 A high school physics teacher wondered if his students in the senior class this year will be more likely to go into STEM (Science, Technology, Engineering, Mathematics) majors than Social Science and Liberal Arts majors. He asked each of his 72 students about their first choice for major on their college applications and conducted a Chi-square test for goodness of fit with an alpha level of .05 to see if the number of students choosing each category differs significantly.  20 – STEM  18 – Social Sciences  34 – Liberal Arts a. The variable in this test is the students' first choice for major on their college applications. It is a nominal variable because it represents categories or names without any inherent order or ranking. b. Null hypothesis (H0): The distribution of students' first choice for major is equal across STEM, Social Sciences, and Liberal Arts. Alternative hypothesis (H1): The distribution of students' first choice for major differs across STEM, Social Sciences, and Liberal Arts. c. The calculated Chi-Square statistic is approximately 6.334. d. The degrees of freedom (df) are 2, and the critical value for a significance level of 0.05 is approximately 5.991. e. Since 6.334 > 5.991, we reject the null hypothesis. f. Based on our analysis, we reject the null hypothesis, indicating that the distribution of students' first choice for major differs significantly across STEM, Social Sciences, and Liberal Arts. Q3) Chi-Square Test for Independence (8 points) This question is an extension from Q2 above. The high school teacher was also interested in whether there is a gender difference in terms of the student’s choice of majors. So, he broke down the data for his first period class with 50 students by gender in the following table and conducted a Chi-square test for independence with  = .05. Type of Major Female Male Total STEM 8 12 20 Social Sciences 10 10 20 Liberal Arts 8 2 10 a. The variables in this analysis are the type of major and gender of the students. Type of Major: Nominal variable, representing different categories of majors without any inherent order. Gender: Nominal variable, indicating categories (female and male) without any specific order or ranking. All course content and materials, including this assignment and all other items published within the Canvas course shell, are copyrighted materials and students may not share outside the class, upload to online websites not approved by the instructor, sell, or distribute course content or notes taken during the conduct of the course (see ACD 304–06 , “Commercial Note Taking Services” and ABOR Policy 5-308 F.14 for more information). Students must refrain from uploading to any course shell, discussion board, or website used by the course instructor or other course forum, material that is not the student’s original work, unless the students first comply with all applicable copyright laws; faculty members reserve the right to delete materials on the grounds of suspected copyright infringement.

PSY230_Bienemann Spring 2024 b. Null hypothesis (H0): There is no association between the type of major and gender of the students. Alternative hypothesis (H1): There is an association between the type of major and gender of the students. c. The Chi-Square statistic is approximately 4.327. d. Degrees of Freedom (df) = 2 Critical value for df=2 and α=0.05 is approximately 5.991. e. Since 4.327<5.991, we fail to reject the null hypothesis. f. Based on the Chi-Square test, we do not have enough evidence to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that there is a significant relationship between the type of major and gender of the students at the 5% significance level. Q4) Chi-Square Test for Independence (8 points) A market researcher conducted a study to see if different age groups prefer different news sources. He surveyed 80 people in the 25-49 age group and 80 people in the 50+ age group and asked them if they prefer to get their news from TV, online, radio, or printed newspapers. The data are listed in the table below. Conduct a Chi-Square test for Independence with α = .01. News source Group 18-49 Group 50+ Total count TV 20 30 50 Online 40 20 60 Radio 15 15 30 Printed papers 5 15 20 a. The variables in this analysis are the age group (25-49 and 50+) and the preferred news source (TV, online, radio, printed papers). Both variables are categorical and nominal, as they represent different categories without any inherent order or numerical value. b. Null Hypothesis (H0): There is no association between age group and preferred news source. Alternative Hypothesis (Ha): There is an association between age group and preferred news source. c. X2 statistic = 13.666 d. df = 3; critical value = 11.345 e. Since 13.666>11.345, we reject the null hypothesis. f. Based on the Chi-Square test, we reject the null hypothesis. All course content and materials, including this assignment and all other items published within the Canvas course shell, are copyrighted materials and students may not share outside the class, upload to online websites not approved by the instructor, sell, or distribute course content or notes taken during the conduct of the course (see ACD 304–06 , “Commercial Note Taking Services” and ABOR Policy 5-308 F.14 for more information). Students must refrain from uploading to any course shell, discussion board, or website used by the course instructor or other course forum, material that is not the student’s original work, unless the students first comply with all applicable copyright laws; faculty members reserve the right to delete materials on the grounds of suspected copyright infringement.

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PSY230_Bienemann Spring 2024 This means that there is a significant association between age group and preferred news source among the surveyed population at the α=0.01 significance level. All course content and materials, including this assignment and all other items published within the Canvas course shell, are copyrighted materials and students may not share outside the class, upload to online websites not approved by the instructor, sell, or distribute course content or notes taken during the conduct of the course (see ACD 304–06 , “Commercial Note Taking Services” and ABOR Policy 5-308 F.14 for more information). Students must refrain from uploading to any course shell, discussion board, or website used by the course instructor or other course forum, material that is not the student’s original work, unless the students first comply with all applicable copyright laws; faculty members reserve the right to delete materials on the grounds of suspected copyright infringement.

PSY230_M7_Assignment_Spring2024

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