Course Hero Logo

Assignment4.pdf - COR-STAT 1203 Introduction to Statistical...

Course Hero uses AI to attempt to automatically extract content from documents to surface to you and others so you can study better, e.g., in search results, to enrich docs, and more. This preview shows page 1 - 3 out of 3 pages.

1COR-STAT 1203 Introduction to Statistical Theory, G3-G4, Term II, 2021-22Assignment 4Due date and time:Friday 11.59pm,Week 11(March 25, 2022)Place to submit:eLearnā†’Assignmentsā†’Assignment 4Instructions:(i)Write yournameandgroup numberclearly on the top of the first page;(ii)Convert your solutions into one pdf file named:YourName_A4_GroupNo.pdf,e.g., GohZhiHui_A4_G3.pdf, TayAlbert_A4_G4.pdf;(iii) Late assignment will not be accepted, andzero markwill be given to two or morevery similar assignments;(iv) You may do the assignment by handwriting onA4-size paperā†’scanā†’pdf;or typing by word (or some other software, with A4 page specification)ā†’pdf;(v) Minimize the size of the pdf file for submission.1.A random sampleX1,X2, ā€¦,Xnof sizenis taken from an exponential distributionwith meanĪ².LetXbe the sample mean.(a)Show thatš‘‹š‘‹ļæ½is an unbiased estimator ofĪ²(b)Show that Var(š‘‹š‘‹ļæ½) =š›½š›½2š‘›š‘›ā„(c)Based on a random sample of sizen= 50,š‘‹š‘‹ļæ½is observed to be 12.Give anapproximate 95% confidence interval forĪ²2.The heights of a random sample of 50 college students showed a mean of 174.5centimeters and a standard deviation of 6.9 centimeters.(a)Construct a 95% confidence interval (C.I.) for the mean height of all collegestudents.(b)What can we assert with 95% confidence about the possible size of our errorif we estimate the mean height of all college students to be 174.5 centimeters?(c)Construct a 99% C.I. for the mean height of all college students. Comparewith the 95% C.I. obtained in (a) and comment.3.The following measurements were recorded for the drying time, in hours, of acertain brand of latex paint:3.4, 2.5, 4.8, 2.9, 3.6, 2.8, 3.3, 5.6, 3.7, 2.8, 4.4, 4.0, 5.2, 3.0, 4.8.(a)Provide point estimates for the population mean and standard deviation of thedrying time.(b)Assuming the measurements represent a random sample from a normalpopulation, find a 90% confidence interval and a 95% confidence interval forthe population mean drying time.(c)Suppose that it is known (from previous studies) that the population standarddeviation of drying timeĻƒ= 1. How large a sample will be needed in order forthe sample mean to be within 0.2 hour of the true mean with 95% confidence?...
COR-STAT1203 A4

Upload your study docs or become a

Course Hero member to access this document

End of preview. Want to read all 3 pages?

Upload your study docs or become a

Course Hero member to access this document

Term
Spring
Professor
NoProfessor

Newly uploaded documents

Show More

Newly uploaded documents

Show More

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture