Question
1. Return to the US News dataset on Tier I National Universities.
2. Perform a t test the difference in mean PeerRating, HSGCRating, GradRate and AlumSalary between public and private schools using a .05 level of significance.
3. Perform an ANOVA test of the differences in mean PeerRating and HSGCRating by levels of Selectivity using a .05 level of significance.
4. For the crosstabulation of Selectivity by Type and Region by Type, test the differences between types using chi-square with a .05 level of significance
5. Write a report (in MS Word) describing and interpreting the results of your analyses, inserting the any charts and tables where they belong.
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Excel Output:
F-Test Two-Sample for Variances

Private PeerRating, Public PeerRating
Mean 3.152040816 3.223469388
Variance 0.794274143 0.229237324
Observations 98 98
df 97 97
F 3.46485524
P(F<=f) one-tail 1.5785E-09
F Critical one-tail 1.398866187

t-Test: Two-Sample Assuming Unequal Variances

Private PeerRating, Public PeerRating
Mean 3.152040816 3.223469388
Variance 0.794274143 0.229237324
Observations 98 98
Hypothesized Mean Difference 0
df 149
t Stat -0.698937989
P(T<=t) one-tail 0.242840174
t Critical one-tail 1.655144534
P(T<=t) two-tail 0.485680347
t Critical two-tail 1.976013145

Interpretation:
From the above output, we can see that the variance of Peer Assessment Rating (PeerRating) is not equal between public and private schools because the F-Test Two-Sample for Variances has p-value 0.0000 which is smaller than 0.05 so we will use “t-Test: Two-Sample Assuming Unequal Variances”. The t test output gives the two sided p-value as 0.4856 which is bigger than 0.05, so we can conclude that there is no statistically significant difference in mean Peer Assessment Rating between public and private schools.
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      • Illuminate\Cache\Events\CacheHit (93μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (93μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (90μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (89μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (92μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheMissed (287μs)
      • Illuminate\Database\Events\StatementPrepared (927μs)
      • Illuminate\Database\Events\QueryExecuted (863μs)
      • eloquent.retrieved: App\Models\SubjectCat (63μs)
      • Illuminate\Cache\Events\KeyWritten (267μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (142μs)
      • Illuminate\Cache\Events\CacheHit (290μs)
      • Illuminate\Cache\Events\CacheHit (265μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (305μs)
      • Illuminate\Cache\Events\CacheHit (144μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • creating: site.layouts.app (362μs)
      • composing: site.layouts.app (17μs)
      • creating: components.canonical (372μs)
      • composing: components.canonical (74μs)
      • creating: components.open-graph (135μs)
      • composing: components.open-graph (48μs)
      • creating: site.headers.header (205μs)
      • composing: site.headers.header (59μs)
      • Illuminate\Cache\Events\CacheHit (1.41ms)
      • creating: components.footer (66μs)
      • composing: components.footer (67μs)
      • Illuminate\Cache\Events\CacheHit (744μs)
      • Illuminate\Cache\Events\CacheMissed (367μs)
      • Illuminate\Database\Events\StatementPrepared (858μs)
      • Illuminate\Database\Events\QueryExecuted (1.09ms)
      • eloquent.retrieved: App\Models\SubjectCat (65μs)
      • Illuminate\Cache\Events\KeyWritten (264μs)
      • Illuminate\Cache\Events\CacheHit (292μs)
      • Illuminate\Cache\Events\CacheHit (1.89ms)
      • Illuminate\Cache\Events\CacheHit (6.12ms)
      • Illuminate\Cache\Events\CacheHit (272μs)
      • Illuminate\Cache\Events\CacheHit (151μs)
      • Illuminate\Cache\Events\CacheHit (2.7ms)
      • Illuminate\Cache\Events\CacheHit (292μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • creating: components.forms.contact-us (233μs)
      • composing: components.forms.contact-us (120μs)
      • creating: components.forms.get-started (1.17ms)
      • composing: components.forms.get-started (75μs)
      • creating: components.forms.free-tool-download (113μs)
      • composing: components.forms.free-tool-download (45μs)
      • creating: components.forms.claim-free-worksheet (85μs)
      • composing: components.forms.claim-free-worksheet (42μs)
      • creating: components.forms.tutor-subscription-waitlist (81μs)
      • composing: components.forms.tutor-subscription-waitlist (40μs)
      • creating: components.forms.tutor-subscription-join (79μs)
      • composing: components.forms.tutor-subscription-join (40μs)
      • creating: components.forms.tutor-support (76μs)
      • composing: components.forms.tutor-support (39μs)
      • 311 x Illuminate\Cache\Events\CacheHit (18.66%)
        71.33ms
        20 x Illuminate\Database\Events\StatementPrepared (11.1%)
        42.43ms
        20 x Illuminate\Database\Events\QueryExecuted (8.09%)
        30.91ms
        11 x Illuminate\Cache\Events\CacheMissed (1.76%)
        6.73ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.23%)
        4.70ms
        11 x Illuminate\Cache\Events\KeyWritten (0.89%)
        3.40ms
        1 x creating: components.forms.get-started (0.31%)
        1.17ms
        1 x Illuminate\Routing\Events\Routing (0.24%)
        907μs
        1 x Illuminate\Database\Events\ConnectionEstablished (0.21%)
        787μs
        12 x eloquent.retrieved: App\Models\SubjectCat (0.18%)
        701μs
        1 x creating: components.canonical (0.1%)
        372μs
        1 x creating: site.layouts.app (0.09%)
        362μs
        1 x eloquent.booting: App\Models\SubjectCat (0.09%)
        350μs
        1 x Illuminate\Routing\Events\RouteMatched (0.09%)
        349μs
        1 x creating: components.breadcrumbs (0.09%)
        336μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.08%)
        305μs
        2 x eloquent.retrieved: App\Models\Subject (0.07%)
        263μs
        1 x creating: homework.show (0.06%)
        248μs
        1 x creating: components.forms.contact-us (0.06%)
        233μs
        10 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.05%)
        208μs
        1 x creating: site.headers.header (0.05%)
        205μs
        1 x eloquent.booting: App\Models\Subject (0.05%)
        173μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        171μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        160μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        148μs
        1 x creating: components.open-graph (0.04%)
        135μs
        1 x composing: homework.show (0.03%)
        128μs
        1 x composing: components.breadcrumbs (0.03%)
        121μs
        1 x composing: components.forms.contact-us (0.03%)
        120μs
        1 x creating: components.forms.free-tool-download (0.03%)
        113μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        85μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        81μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        79μs
        1 x eloquent.booted: App\Models\Subject (0.02%)
        77μs
        1 x creating: components.forms.tutor-support (0.02%)
        76μs
        1 x composing: components.forms.get-started (0.02%)
        75μs
        1 x composing: components.canonical (0.02%)
        74μs
        1 x composing: components.footer (0.02%)
        67μs
        1 x creating: components.footer (0.02%)
        66μs
        1 x composing: site.headers.header (0.02%)
        59μs
        1 x composing: components.open-graph (0.01%)
        48μs
        1 x composing: components.forms.free-tool-download (0.01%)
        45μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        42μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        40μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        40μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        40μs
        1 x composing: components.forms.tutor-support (0.01%)
        39μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        38μs
        1 x composing: site.layouts.app (0%)
        17μs
      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
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 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
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated59.51ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        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
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '46272' limit 1
        25.96mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 46272
        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 (7)
        1.18mstwenty4_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 (46272)
        4.36mstwenty4_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
        900μstwenty4_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` <> 46272 and `subject` = 7 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        10.28mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 46272
        • 1: 7
        • 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 (7)
        860μstwenty4_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` = 46272 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.13mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 46272
        • 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
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 46272 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        980μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 46272
        • 1: teaser
        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
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 46272 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        960μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 46272
        • 1: solution
        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
        960μstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        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` = 1 limit 1
        1.07mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        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` = 3 limit 1
        1.06mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        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
        1.01mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        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
        1.03mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        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
        1.05mstwenty4_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
        960μstwenty4_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
        1.05mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        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
        2.26mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        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
        1.14mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        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
        1.31mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        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
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      10HomeworkLibraryFile.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
          _token
          cWYRh9JPzNv3dsnsXso1hUJodJPWzfn3GMqkvRlf
          utm_source
          direct
          redirectUrl
          /college-homework-library/Mathematics/General-Statistics/46272
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Gen...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Mathematics/General-Statistics/46272
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
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