Question
1. A sample is selected from a population with μ = 50. After a treatment is administered to the individuals in the sample, the mean is found to be M = 55 and the variance is s² = 64.
a. If the sample has n = 4 scores, then conduct a hypothesis test to evaluate the significance of the treatment effect and calculate Cohen’s d to measure the size of the treatment effect. Use a two-tailed test with α = .05.
b. If the sample has n = 16 scores, then conduct a hypothesis test to evaluate the significance of the treatment effect and calculate Cohen’s d to measure the size of the treatment effect. Use a two-tailed test with α = .05.
c. Describe how increasing the size of the sample affects the likelihood of rejecting the null hypothesis and the measure of effect size.

2. A sample of n = 16 indivduals is selected from a population with μ = 30. After a treatment is administered to the individuals, the sample mean is found to be M = 33.
a. If the sample variance is s² = 16, then conduct a hypothesis test to evaluate the significance of the treatment effect and calculate r² to measure the size of the treatment effect. Use a two-tailed test with α = .05.
b. If the sample variance is s² = 64, then conduct a hypothesis test to evaluate the significance of the treatment effect and calculate r² to measure the size of the treatment effect. Use a two-tailed test with α = .05.
c. Describe how increasing variance affects the likelihood of rejecting the null hypothesis and the measure of effect size.

3. A sample of n = 16 scores has a mean of M = 58 with SS = 960. Use the sample to construct the 90% confidence interval for μ.

4. A sample of n = 9 participants is obtained from a population with μ = 29, and a treatment is administered to the individuals in the sample. After treatment, the scores for the nine participants are as follows: 23, 33, 26, 28, 30, 26, 27, 25, 25.      
a. Are the data sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05.
b. Are the data sufficient to conclude that the treatment significantly decreased scores? Use a one-tailed test with α = .05.

5. Although you can compute a z-score for a single score (a sample of n = 1), it is impossible to compute a t statistic for a sample that has only one score. Explain why.
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        Backtrace
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        Backtrace
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        • 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
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        1.08mstwenty4_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
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        910μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
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        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        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
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        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
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        • 18. app/Repositories/HomeworkLibraryRepository.php:39
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      • select * from `subjects` where `subjects`.`id` in (7)
        960μstwenty4_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` = 24358 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.93mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        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
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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