Your Perfect Assignment is Just a Click Away

Starting at $8.00 per Page

100% Original, Plagiarism Free, Customized to Your instructions!

glass
pen
clip
papers
heaphones

STATS 120C University of California Week 6 Probability Statistics Questions

STATS 120C University of California Week 6 Probability Statistics Questions

Question Description

1. Consider the one-way unbalanced groups ANOVA model

page1image10848

yij = μi ijiid 2

with i = 1,…,I; j = 1,…,Ji and εij N(0,σ ).
Assume the I groups are independent and ∑Ii=1 αi = 0. Consider the contrastL = ∑Ii=1 ciμi, and suppose we want to test H0 : L = 0 versus the alternative

H1 :LConsider the test statistics

where Lˆ = ∑Ii=1 ciȳi·, MSE denotes the Mean Square Error in the ANOVA table associated with the I groups of the one-way ANOVA model. Show that under the null hypothesis H0 : L = 0, the test statistic t follows a t– distribution with ∑Ii=1 Ji I degrees of freedom.

2. Arehabilitationcenterresearchwasinterestedinexaminingtherelationship between physical fitness prior to surgery of persons undergoing corrective knee surgery and time required in physical therapy until successful reha- bilitation. Patient records in the rehabilation center were examined, and 24 male subjects ranging in age from 18 to 30 years had undergone simi- lar corrective knee surgery during the past year were selected for the study. The number of days required for succesful completion of physical therapy and the prior physical fitness status (below average, average, above average, etc.) for each patient follows:

Observation ( j) Pre-surgerystatus 1 2 3 4 5 6 7 8 9 10

Lˆt=Ic2i

page2image9856page2image10016

MSE·∑i=1 Ji

page2image10664page2image10824page2image10984page2image11144

Poor BelowAverage Average AboveAverage Excellent

443843484447 29 42 38 40 43 40 303539283131 26 32 21 20 23 22 141822211720

42  45  45  4330  4229  35  29  33

20 28

page2image14872

(a) Suppose that we wish to determine whether or not the mean rehabil- itation time in patients with a ’Poor’ or ’Below Average’ pre-surgery health status is different from the mean rehabilitation time in patients in any of the other pre-surgery groups. State the appropriate null and alternative hypothesis for this question.

  1. (b) Carry out a test of the hypothesis stated in (a). State what test statistic you are using, and provide all the necessary information used to cal- culate the test statistic (e.g. show ALL your work). Report the value of the test statistic, calculate the p-value, state your decision, and in- terpret the results of your test in a way that would be understandable to a non-statician.
  2. (c) Form simultaneous 95% confidence intervals for the difference in the mean rehabilation time of:
    1. patients with a ’Poor’ pre-surgery health status versus that a pa- tients with a ’Average’ pre-squrger health status;
    2. patients with a ’Poor’ pre-surgery health status versus that a pa- tients with a ’Above Average’ pre-squrger health status;
    3. patients with a ’Poor’ pre-surgery health status versus that a pa- tients with a ’Excellent’ pre-squrger health status;


"Place your order now for a similar assignment and have exceptional work written by our team of experts, guaranteeing you A results."

Order Solution Now

Our Service Charter


1. Professional & Expert Writers: Eminence Papers only hires the best. Our writers are specially selected and recruited, after which they undergo further training to perfect their skills for specialization purposes. Moreover, our writers are holders of masters and Ph.D. degrees. They have impressive academic records, besides being native English speakers.

2. Top Quality Papers: Our customers are always guaranteed of papers that exceed their expectations. All our writers have +5 years of experience. This implies that all papers are written by individuals who are experts in their fields. In addition, the quality team reviews all the papers before sending them to the customers.

3. Plagiarism-Free Papers: All papers provided by Eminence Papers are written from scratch. Appropriate referencing and citation of key information are followed. Plagiarism checkers are used by the Quality assurance team and our editors just to double-check that there are no instances of plagiarism.

4. Timely Delivery: Time wasted is equivalent to a failed dedication and commitment. Eminence Papers are known for the timely delivery of any pending customer orders. Customers are well informed of the progress of their papers to ensure they keep track of what the writer is providing before the final draft is sent for grading.

5. Affordable Prices: Our prices are fairly structured to fit in all groups. Any customer willing to place their assignments with us can do so at very affordable prices. In addition, our customers enjoy regular discounts and bonuses.

6. 24/7 Customer Support: At Eminence Papers, we have put in place a team of experts who answer all customer inquiries promptly. The best part is the ever-availability of the team. Customers can make inquiries anytime.