# Answer in Statistics and Probability for Goldie #254471

A sleep researcher conducts an experiment to determine whether sleep loss affects the ability to maintain sustained attention. Fifteen individuals are randomly divided into the following three groups of five subjects each: group 1, which gets the normal amount of sleep (7–8 hours); group 2, which is sleep-deprived for 24 hours; and group 3, which is sleep-deprived for 48 hours. All three groups are tested on the same auditory vigilance task. Subjects are presented with half-second tones spaced at irregular intervals over 1-hour duration. Occasionally, one of the tones is slightly shorter than the rest. The subject’s task is to detect the shorter tones. The following percentages of correct detection were observed:

Normal Sleep: 85 83 76 64 75

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Answer in Statistics and Probability for Goldie #254471
Just from $13/Page Sleep-Deprived for 24-hours: 60 58 76 52 63 Sleep-Deprived for 48-hours: 60 48 38 47 50 Determine whether there is an overall effect for sleep deprivation, using the conceptual equations of the one-way ANOVA. Use ∝= 0.05. totals Normal Sleep: 85 83 76 64 75 383 Sleep-Deprived for 24-hours: 60 58 76 52 63 309 Sleep-Deprived for 48-hours: 60 48 38 47 50 243 Total 935 “n=15” The correction factor, “CF={935^2\over 15}=58281.67” Total sum of squares. “TSS=(85^2+83^2+76^2+…….+47^2+50^2)- 58281.67= 61081-58281.67=2799.33” Treatment sum of squares. “TRSS=({383^2+309^2+243^2\over4})-58281.67=60243.8-58281.67=1962.13” Error sum of squares “ESS=TSS-TRSS=2799.33-1962.13=837.2” Degrees of freedom For this case, “n=15,k=3” For the treatments, degrees of freedom is k-1=3-1=2 For the error, degrees of freedom is n-k=15-3=12 Hypotheses “H_0:\mu_1=\mu_2=\mu_3\\vs\\ H_1: At\space least \space one \space is \space different” ANOVA table source degrees of freedom sum of squares mean squares F Treatments 2 1962.13 “{1962.13\over2}=981.065” 14.062 Error 12 837.2 “{837.2\over12}=69.77” Total 14 2799.33 Critical value, “F_{0.05, 2,12}=3.885294” Decision criteria Reject “H_0” if “F\gt F_{0.05,2,12}” Since, “F=14.062\gt F_{0.05,2,12}=3.885294”, the null hypothesis is rejected and conclude that, there is sufficient evidence to support the claim that sleep deprivation appears to affect sustained attention at 5% level of significance. # What Will You Get? We provide professional writing services to help you score straight A’s by submitting custom written assignments that mirror your guidelines. #### Premium Quality Get result-oriented writing and never worry about grades anymore. We follow the highest quality standards to make sure that you get perfect assignments. #### Experienced Writers Our writers have experience in dealing with papers of every educational level. You can surely rely on the expertise of our qualified professionals. #### On-Time Delivery Your deadline is our threshold for success and we take it very seriously. We make sure you receive your papers before your predefined time. #### 24/7 Customer Support Someone from our customer support team is always here to respond to your questions. So, hit us up if you have got any ambiguity or concern. #### Complete Confidentiality Sit back and relax while we help you out with writing your papers. We have an ultimate policy for keeping your personal and order-related details a secret. #### Authentic Sources We assure you that your document will be thoroughly checked for plagiarism and grammatical errors as we use highly authentic and licit sources. #### Moneyback Guarantee Still reluctant about placing an order? Our 100% Moneyback Guarantee backs you up on rare occasions where you aren’t satisfied with the writing. #### Order Tracking You don’t have to wait for an update for hours; you can track the progress of your order any time you want. We share the status after each step. #### Areas of Expertise Although you can leverage our expertise for any writing task, we have a knack for creating flawless papers for the following document types. # Trusted Partner of 9650+ Students for Writing From brainstorming your paper's outline to perfecting its grammar, we perform every step carefully to make your paper worthy of A grade. ##### Preferred Writer Hire your preferred writer anytime. Simply specify if you want your preferred expert to write your paper and we’ll make that happen. ##### Grammar Check Report Get an elaborate and authentic grammar check report with your work to have the grammar goodness sealed in your document. ##### One Page Summary You can purchase this feature if you want our writers to sum up your paper in the form of a concise and well-articulated summary. ##### Plagiarism Report You don’t have to worry about plagiarism anymore. Get a plagiarism report to certify the uniqueness of your work. ## Free Features$66FREE

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