RMcCormick_Module 05_020424

docx

School

St. Petersburg College *

*We aren’t endorsed by this school

Course

1625

Subject

Statistics

Date

Feb 20, 2024

Type

docx

Pages

Uploaded by CountJellyfishMaster998

Module 05 Assignment Hypothesis Testing Rhonda McCormick Rasmussen University G163/STA1625 Section 03 Essential Statistics and Analytics Instructor: Nigel Basta 02/04/24

Hypothesis Testing Part One: Hypothesis Test - Situation 1 It has been reported that the mean amount of sleep that adults receive is 7 hours per night. Your boss has asked you to look into this statistic by running your own study. You gather 49 adults and find the following information. The mean amount of sleep was 6.2 hours with a standard deviation of 1.8 hours. Based on your results, you claim that adults receive less than 7 hours of sleep. Test your claim with a 0.05 significance level. Null Hypothesis H 0 : μ = 7 hours (Mean amount of sleep is 7 hours) Alternative Hypothesis H a : μ < 7 hours (Mean amount of sleep is less than 7 hours) Significance level (α) = 0.05 We can use the z-test for means since the sample size is larger than 30. Decision Rule: For a one-tailed test (less than), the critical value for a 0.05 significance level is -1.645. Sample mean ( ) = 6.2 hours x̄ Sample standard deviation (s) = 1.8 hours Sample size (n) = 49 Test statistics compared to critical value: -3.11 < -1.645, we reject the null hypothesis. P-value method: P(Z<−3.11) There is enough evidence to reject the null hypothesis. The mean amount of sleep for adults is less than 7 hours per night. Hypothesis Tests - Situation 2 Your boss also would like you to look at average sleep for a specific age range (between 35 and 44 years of age). It has been previously reported that 38.3% of adults in this age range receive the recommended

amount of sleep per night (at least 7 hours). You decide to test this claim by gathering 32 adults between the ages of 35 and 44 years old. In the sample, you find that 15 of the participants receive at least 7 hours of sleep. Test the claim that more than 38.3% of adults get the recommended amount of sleep per night with a significance level of 0.01. Null Hypothesis H 0 : p ≤ 0.383 (Proportion is 38.3% or less) Alternative Hypothesis H 1 : p > 0.383 (Proportion is more than 38.3%) Significance level (α) = 0.01 The critical value for a 0.01 significance level is approximately 2.33 Sample proportion ( ) = 15/32 ≈ 0.46875 (15 participants out of 32 received at least 7 hours of sleep) p̂ Population proportion under the null hypothesis (p) = 0.383 Sample size (n) = 32 Since 1.049 < 2.33, we fail to reject the null hypothesis. P-Value Method: P(Z>1.049) Since the p-value (>0.01) is more than the significance level, you fail to reject the null hypothesis. There is not enough evidence to reject the null hypothesis. Part Two: After you have completed your hypothesis tests, in a separate paragraph,  Explain the possible error(s) that could have occurred and what they imply for each test.  Explain how you might prevent the error(s) from occurring in future hypothesis tests. Testing hypotheses involves potential errors, specifically Type I and Type II errors. Type I errors happen when the null hypothesis is incorrectly rejected, impacting the research findings and subsequent planning. In the first hypothesis (Situation 1), such an error would lead to misguided conclusions with repercussions for future research. In the second hypothesis (Situation 2), an incorrect rejection of the

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

null hypothesis would alter the perceived proportion of adults, influencing the research outcomes. Decreasing the significance level helps mitigate the risk of Type I errors. On the other hand, Type II errors occur when the null hypothesis is not rejected when it is actually incorrect. This can result from small sample sizes and high data variability. In the first hypothesis (Situation 1), a Type II error would lead to the erroneous conclusion that adults sleep an average of seven hours, hindering further planning and research initiatives by the company. For Situation 2 (hypothesis two), a Type II error would result in the rejection of the company's claim, impacting future research and development plans. Increasing the sample size can help reduce the likelihood of Type II errors.

Related Documents

AMS 310 Spring 2024 HW 1 .docx

stat_exam2A_solutions_spring14.pdf

CRJU3610_Problem Set_2 new Answer Key.docx

Tox Hw 2.xlsx

4.15.PNG

RMcCormick_Module 04 Applying Game Theory_012824.docx

RMcCormick_Module 03 Assignment_012123.docx

RMcCormick_Module 02 Graphs and Measures_011424.pptx

Testing_Correlations.pdf

Lab4.pdf

ISL-exam#2-lab-practice.pdf

Decision Tree - Cross Validation.pdf

Recommended textbooks for you

Glencoe Algebra 1, Student Edition, 9780079039897...

Algebra

ISBN:9780079039897

Author:Carter

Publisher:McGraw Hill

Holt Mcdougal Larson Pre-algebra: Student Edition...

Algebra

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

College Algebra (MindTap Course List)

Algebra

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:Cengage Learning

SEE MORE TEXTBOOKS

Recommended textbooks for you

Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning