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10. A random sample of enrollments from medical schools that specialize in research and from those that are noted for primary care is listed. At a = 0.01 is there sufficient evidence to conclude that there is a difference in average enrollment based on the sample data? Research Primary Care 474 783 813 692 884 577 467 443 694 605 670 565 277 663 414 696 419 783 546 442 662 605 474 587 555 427 371 293 527 728 107 277 320

10. A random sample of enrollments from medical schools that specialize in research and from those that are noted for primary care is listed. At a = 0.01 is there sufficient evidence to conclude that there is a difference in average enrollment based on the sample data? Research Primary Care 474 783 813 692 884 577 467 443 694 605 670 565 277 663 414 696 419 783 546 442 662 605 474 587 555 427 371 293 527 728 107 277 320

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A random sample of enrollments from medical schools that specialize in research and from
those that are noted for primary care is listed. At a = 0.01 is there sufficient evidence to
conclude that there is a difference in average enrollment based on the sample data?

Research

474

783

813

692

884

577

605

467

670

443

565

694

277

663

414

696

419

783

546

442

662

605

427

474

371

587

293

555

527

728

107

277

320

**Analysis of Medical School Enrollments: Research vs. Primary Care** This exercise involves a random sample of enrollments from medical schools that specialize in research and those noted for primary care. Our goal is to determine if there is a significant difference in average enrollments between the two groups using a significance level of α = 0.01. **Data Presented:** - **Research-focused Enrollments:** - 474 - 577 - 605 - 653 - 783 - 813 - **Primary Care-focused Enrollments:** - 320 - 527 - 555 - 662 - 728 - 884 **Analysis Steps:** 1. **Average Enrollment Calculation:** - Compute the mean enrollment for both research and primary care groups. 2. **Variance and Standard Deviation:** - Calculate the variance and standard deviation to understand the spread and consistency of enrollments within each category. 3. **Hypothesis Testing:** - Null Hypothesis (H0): There is no difference in average enrollments between the two groups. - Alternative Hypothesis (H1): There is a difference in average enrollments between the two groups. 4. **Statistical Test:** - Use a two-sample t-test to compare the means of the two independent samples. This test is appropriate given that the enrollments come from two different types of medical schools and we're examining if their averages differ significantly. 5. **Conclusion:** - Determine if the p-value from the t-test is less than the significance level (α = 0.01). If so, we reject the null hypothesis in favor of the alternative. By conducting this analysis, educators and students can understand the statistical techniques involved in comparing two sample groups and draw conclusions regarding the differences in enrollments based on specialization.
Transcribed Image Text:**Analysis of Medical School Enrollments: Research vs. Primary Care** This exercise involves a random sample of enrollments from medical schools that specialize in research and those noted for primary care. Our goal is to determine if there is a significant difference in average enrollments between the two groups using a significance level of α = 0.01. **Data Presented:** - **Research-focused Enrollments:** - 474 - 577 - 605 - 653 - 783 - 813 - **Primary Care-focused Enrollments:** - 320 - 527 - 555 - 662 - 728 - 884 **Analysis Steps:** 1. **Average Enrollment Calculation:** - Compute the mean enrollment for both research and primary care groups. 2. **Variance and Standard Deviation:** - Calculate the variance and standard deviation to understand the spread and consistency of enrollments within each category. 3. **Hypothesis Testing:** - Null Hypothesis (H0): There is no difference in average enrollments between the two groups. - Alternative Hypothesis (H1): There is a difference in average enrollments between the two groups. 4. **Statistical Test:** - Use a two-sample t-test to compare the means of the two independent samples. This test is appropriate given that the enrollments come from two different types of medical schools and we're examining if their averages differ significantly. 5. **Conclusion:** - Determine if the p-value from the t-test is less than the significance level (α = 0.01). If so, we reject the null hypothesis in favor of the alternative. By conducting this analysis, educators and students can understand the statistical techniques involved in comparing two sample groups and draw conclusions regarding the differences in enrollments based on specialization.
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