Question
Describe a situation where you would use a Chi-squared test by stating
1. your sample and two variables or two samples and one variable,
2. whether or not the test would be one of homogeneity or independence,
3. Both a null and an alternative hypotheses, and
4. a significance level. Then find
5. the degrees of freedom of your chi-squared statistic,
6. the rejection region for your test and state
7. what a chi-squared statistic value in this region would imply for your test. Remember that you do not need to list the values of the variable for individuals in either the samples or the population, and that the value for 4 does not need to be calculated, only stated.
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Forensic Science
Both instances can actually be compared based on the glass. The initial analysis of a glass description is based on many factors such as color, thickness and florescence. Upon further review, the two samples can be can be compared based on the remains of trace elements existing in small amounts. The composition can also differ between the samples. If you find similarities between the two samples can potentially help in solving two crimes with a similar suspect if the composition is the same. Small shard glass samples can also be considered evidence in the area of forensic science.
Statistics

Describe a situation where you would use a Chi-squared test by stating

1. Sample and two variables or two samples and one variable
A group of female and female high school freshmen picking their favorite class out of Math, English, and Gym
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      • Illuminate\Cache\Events\KeyWritten (295μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (371μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (154μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • creating: site.layouts.app (482μs)
      • composing: site.layouts.app (23μs)
      • creating: components.canonical (372μs)
      • composing: components.canonical (109μs)
      • creating: components.open-graph (183μs)
      • composing: components.open-graph (77μs)
      • creating: site.headers.header (260μs)
      • composing: site.headers.header (89μs)
      • Illuminate\Cache\Events\CacheHit (1.89ms)
      • creating: components.footer (74μs)
      • composing: components.footer (86μs)
      • Illuminate\Cache\Events\CacheHit (902μs)
      • Illuminate\Cache\Events\CacheMissed (411μs)
      • Illuminate\Database\Events\StatementPrepared (1.03ms)
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      • Illuminate\Cache\Events\KeyWritten (1.55ms)
      • Illuminate\Cache\Events\CacheHit (509μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (243μs)
      • Illuminate\Cache\Events\CacheHit (253μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (330μs)
      • Illuminate\Cache\Events\CacheHit (367μs)
      • Illuminate\Cache\Events\CacheHit (250μs)
      • Illuminate\Cache\Events\CacheHit (253μs)
      • Illuminate\Cache\Events\CacheHit (243μs)
      • Illuminate\Cache\Events\CacheHit (253μs)
      • Illuminate\Cache\Events\CacheHit (240μs)
      • creating: components.forms.contact-us (240μs)
      • composing: components.forms.contact-us (176μs)
      • creating: components.forms.get-started (149μs)
      • composing: components.forms.get-started (79μs)
      • creating: components.forms.free-tool-download (109μs)
      • composing: components.forms.free-tool-download (171μs)
      • creating: components.forms.claim-free-worksheet (128μs)
      • composing: components.forms.claim-free-worksheet (72μs)
      • creating: components.forms.tutor-subscription-waitlist (110μs)
      • composing: components.forms.tutor-subscription-waitlist (68μs)
      • creating: components.forms.tutor-subscription-join (105μs)
      • composing: components.forms.tutor-subscription-join (70μs)
      • creating: components.forms.tutor-support (170μs)
      • composing: components.forms.tutor-support (74μs)
      • 312 x Illuminate\Cache\Events\CacheHit (23.33%)
        86.57ms
        19 x Illuminate\Database\Events\StatementPrepared (8.92%)
        33.09ms
        19 x Illuminate\Database\Events\QueryExecuted (7.02%)
        26.06ms
        10 x Illuminate\Cache\Events\KeyWritten (1.99%)
        7.39ms
        10 x Illuminate\Cache\Events\CacheMissed (1.4%)
        5.18ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.26%)
        4.68ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.32%)
        1.19ms
        1 x Illuminate\Routing\Events\Routing (0.29%)
        1.06ms
        11 x eloquent.retrieved: App\Models\SubjectCat (0.26%)
        978μs
        2 x eloquent.retrieved: App\Models\Subject (0.19%)
        708μs
        1 x creating: site.layouts.app (0.13%)
        482μs
        1 x Illuminate\Routing\Events\RouteMatched (0.12%)
        458μs
        1 x creating: homework.show (0.1%)
        381μs
        1 x creating: components.canonical (0.1%)
        372μs
        1 x creating: components.breadcrumbs (0.1%)
        356μs
        1 x creating: site.headers.header (0.07%)
        260μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.07%)
        259μs
        1 x eloquent.booting: App\Models\SubjectCat (0.07%)
        245μs
        1 x creating: components.forms.contact-us (0.06%)
        240μs
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        231μs
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        1 x creating: components.open-graph (0.05%)
        183μs
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        176μs
        1 x composing: components.forms.free-tool-download (0.05%)
        171μs
        1 x creating: components.forms.tutor-support (0.05%)
        170μs
        1 x composing: components.breadcrumbs (0.05%)
        169μs
        8 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.05%)
        168μs
        1 x composing: homework.show (0.04%)
        161μs
        1 x creating: components.forms.get-started (0.04%)
        149μs
        1 x creating: components.forms.claim-free-worksheet (0.03%)
        128μs
        1 x eloquent.booting: App\Models\Subject (0.03%)
        110μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.03%)
        110μs
        1 x creating: components.forms.free-tool-download (0.03%)
        109μs
        1 x composing: components.canonical (0.03%)
        109μs
        1 x creating: components.forms.tutor-subscription-join (0.03%)
        105μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        102μs
        1 x composing: site.headers.header (0.02%)
        89μs
        1 x composing: components.footer (0.02%)
        86μs
        1 x composing: components.forms.get-started (0.02%)
        79μs
        1 x composing: components.open-graph (0.02%)
        77μs
        1 x creating: components.footer (0.02%)
        74μs
        1 x composing: components.forms.tutor-support (0.02%)
        74μs
        1 x composing: components.forms.claim-free-worksheet (0.02%)
        72μs
        1 x composing: components.forms.tutor-subscription-join (0.02%)
        70μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.02%)
        68μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        56μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        43μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        39μs
        1 x composing: site.layouts.app (0.01%)
        23μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
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      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
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      app/Http/Controllers/HomeworkLibraryController.php:79-176
      19 statements were executed, 4 of which were duplicates, 15 unique. Show only duplicated44.73ms
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        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
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        15.04mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
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        • 1: 0
        • 2: 34363
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (124)
        1.31mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (34363)
        1.25mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.13mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 34363 and `subject` = 124 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        3.86mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 34363
        • 1: 124
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (124)
        1.07mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 34363 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.2mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 34363
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
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        1.02mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        5.38mstwenty4_siteHomeworkLibrary.php#201
        Bindings
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        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.63mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        980μstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        2.42mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.18mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.23mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.06mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.16mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.23mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.47mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      11SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      8HomeworkLibraryFile.php
      App\Models\HomeworkLibrary\HomeworkLibrary
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      App\Models\Subject
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