Question
ZIPPY MOTORS and the EPA
The EPA questions the report it received from the Zippy Motor Company. The Zippy Company claimed that the motors it has produced are in compliance with the EPA maximum noise emission of 15dB. Zippy has produced 867 motors and cannot ship them until they are approved by the EPA for noise level compliance.

Rather than test each one, they have tested two random samples with results as follows:
Sample A   
Size 32
Mean 14.9 dB   

Sample B   
Size 34
Mean 14.7 dB

The EPA examined several motors and doubted the validity of Zippy’s tests, so it tested the entire lot with the following results:
Entire Lot
Size 867
Mean 15.6 dB
Std Dev 0.6 dB

What is the likelihood of the results of the two random samples reported by Zippy? What do you suspect Zippy did to obtain those results?

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Problem: Population mean is μ=15.6 and population standard deviation is σ=0.6. Two samples were obtained: Sample 1 (mean m1=14.9, sample size=n1= 32), Sample 2 (mean m2=14.7, sample size=n1= 34). We want to find the probability of obtaining those two samples on a random draw of samples. Based on that, we need to decide if there was any
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      • Illuminate\Cache\Events\CacheMissed (203μs)
      • Illuminate\Database\Events\StatementPrepared (915μs)
      • Illuminate\Database\Events\QueryExecuted (1.48ms)
      • eloquent.retrieved: App\Models\SubjectCat (72μs)
      • Illuminate\Cache\Events\KeyWritten (272μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (291μs)
      • Illuminate\Cache\Events\CacheHit (147μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (134μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (225μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (327μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • creating: site.layouts.app (946μs)
      • composing: site.layouts.app (21μs)
      • creating: components.canonical (523μs)
      • composing: components.canonical (186μs)
      • creating: components.open-graph (447μs)
      • composing: components.open-graph (89μs)
      • creating: site.headers.header (359μs)
      • composing: site.headers.header (79μs)
      • Illuminate\Cache\Events\CacheHit (3.44ms)
      • creating: components.footer (99μs)
      • composing: components.footer (107μs)
      • Illuminate\Cache\Events\CacheHit (1.22ms)
      • Illuminate\Cache\Events\CacheMissed (755μs)
      • Illuminate\Database\Events\StatementPrepared (5.51ms)
      • Illuminate\Database\Events\QueryExecuted (1.1ms)
      • eloquent.retrieved: App\Models\SubjectCat (84μs)
      • Illuminate\Cache\Events\KeyWritten (341μs)
      • Illuminate\Cache\Events\CacheHit (333μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (142μs)
      • Illuminate\Cache\Events\CacheHit (149μs)
      • Illuminate\Cache\Events\CacheHit (307μs)
      • Illuminate\Cache\Events\CacheHit (251μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (144μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • creating: components.forms.contact-us (250μs)
      • composing: components.forms.contact-us (116μs)
      • creating: components.forms.get-started (139μs)
      • composing: components.forms.get-started (47μs)
      • creating: components.forms.free-tool-download (88μs)
      • composing: components.forms.free-tool-download (40μs)
      • creating: components.forms.claim-free-worksheet (83μs)
      • composing: components.forms.claim-free-worksheet (40μs)
      • creating: components.forms.tutor-subscription-waitlist (81μs)
      • composing: components.forms.tutor-subscription-waitlist (37μs)
      • creating: components.forms.tutor-subscription-join (79μs)
      • composing: components.forms.tutor-subscription-join (38μs)
      • creating: components.forms.tutor-support (78μs)
      • composing: components.forms.tutor-support (38μs)
      • 311 x Illuminate\Cache\Events\CacheHit (16.13%)
        78.04ms
        20 x Illuminate\Database\Events\StatementPrepared (11.72%)
        56.70ms
        20 x Illuminate\Database\Events\QueryExecuted (6.82%)
        33.00ms
        11 x Illuminate\Cache\Events\CacheMissed (1.84%)
        8.92ms
        11 x Illuminate\Cache\Events\KeyWritten (0.93%)
        4.48ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.87%)
        4.21ms
        1 x Illuminate\Routing\Events\Routing (0.24%)
        1.16ms
        1 x creating: site.layouts.app (0.2%)
        946μs
        12 x eloquent.retrieved: App\Models\SubjectCat (0.19%)
        923μs
        1 x Illuminate\Database\Events\ConnectionEstablished (0.16%)
        784μs
        1 x Illuminate\Routing\Events\RouteMatched (0.15%)
        741μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.11%)
        539μs
        1 x creating: components.canonical (0.11%)
        523μs
        1 x creating: components.open-graph (0.09%)
        447μs
        1 x creating: homework.show (0.09%)
        439μs
        1 x creating: site.headers.header (0.07%)
        359μs
        1 x eloquent.booting: App\Models\SubjectCat (0.06%)
        306μs
        1 x creating: components.breadcrumbs (0.05%)
        259μs
        1 x creating: components.forms.contact-us (0.05%)
        250μs
        2 x eloquent.retrieved: App\Models\Subject (0.05%)
        245μs
        1 x composing: components.canonical (0.04%)
        186μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        167μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        159μs
        5 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        143μs
        1 x composing: components.breadcrumbs (0.03%)
        143μs
        1 x creating: components.forms.get-started (0.03%)
        139μs
        1 x composing: homework.show (0.03%)
        130μs
        1 x composing: components.forms.contact-us (0.02%)
        116μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        113μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        113μs
        1 x composing: components.footer (0.02%)
        107μs
        1 x creating: components.footer (0.02%)
        99μs
        1 x composing: components.open-graph (0.02%)
        89μs
        1 x creating: components.forms.free-tool-download (0.02%)
        88μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        83μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        81μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        79μs
        1 x composing: site.headers.header (0.02%)
        79μs
        1 x creating: components.forms.tutor-support (0.02%)
        78μs
        1 x composing: components.forms.get-started (0.01%)
        47μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        44μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        42μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        41μs
        1 x composing: components.forms.free-tool-download (0.01%)
        40μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        40μs
        1 x composing: components.forms.tutor-support (0.01%)
        38μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        38μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        37μs
        1 x composing: site.layouts.app (0%)
        21μs
      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 duplicated69.76ms
      • 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` = '31768' limit 1
        27.38mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 31768
        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)
        1.15mstwenty4_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 (31768)
        990μstwenty4_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
        1.14mstwenty4_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` <> 31768 and `subject` = 7 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        10.83mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 31768
        • 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)
        1.3mstwenty4_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` = 31768 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.18mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 31768
        • 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` = 31768 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.1mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 31768
        • 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` = 31768 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.14mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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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
        1.67mstwenty4_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
        1.21mstwenty4_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` = 3 limit 1
        1.77mstwenty4_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
        1.19mstwenty4_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
        4.79mstwenty4_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
        1.27mstwenty4_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
        1.64mstwenty4_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
        1.23mstwenty4_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
        1.26mstwenty4_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
        1.58mstwenty4_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
        5.94mstwenty4_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\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      5HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
          zH8gNrQSzXOawo7xakvyyFNsXHwJliowqJ4x5fFX
          utm_source
          direct
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          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Gen...
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          status_text
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          content_type
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          request_request
          []
          
          request_headers
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          request_cookies
          []
          
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