36226 HW 9 solutions

# 36226 HW 9 solutions - Introduction to Statistical...

• Homework Help
• 3
• 100% (1) 1 out of 1 people found this document helpful

This preview shows pages 1–2. Sign up to view the full content.

Introduction to Statistical Inference 36-226 Assignment #9 – Solutions Spring, 2017 Problem #1 (a) H 0 : π = 0 . 50 vs H a : π = 0 . 50 . α = . 01 level test Reject H 0 if | z * | > z α/ 2 = z . 005 = 2 . 575 Data: n = 1003 x = 462 ˆ π = 462 1003 = . 461 Test Statistics: z * 1 = . 461 - . 50 ( . 461)(1 - . 461) 1003 = - . 039 . 01574 = - 2 . 478 or z * 2 = . 461 - . 50 ( . 50)(1 - . 50) 1003 = - . 039 . 01579 = - 2 . 470 Decision: Since | z * 1 = - 2 . 478 | < 2 . 575 or ( | z * 2 = - 2 . 470 | < 2 . 575) , we fail to reject H 0 : π = . 50 at the α = . 01 level. At α = . 01 level, we can not conclude that the proportion of cell phone owners who would use their phone to call for advice about a purchase is different from 50%. (b) p -value = 2 · P ( Z < z * 1 = - 2 . 478) = 2 · ( . 0068) = 0 . 0136 (or if you used z * 2 , p-value = .0132). (c) 99% large sample confidence interval for π : ˆ π ± z . 005 ˆ π (1 - ˆ π ) n . 461 ± 2 . 575 ( . 461)(1 - . 461) 1003 = . 461 ± (2 . 575)( . 01574) [ . 421 , . 502] We are 99% confident that the true proportion of cell phone owners who would use their phone to call for advice about a purchase is between 42.1% and 50.2%. Problem #2 The test statistics for testing H 0 : μ = 475 versus H a : μ > 475 is z * = ¯ x - 475 100 / n . We will use the p -value that corresponds to each test to determine whether there is sufficient evidence to reject H 0 . (a) z * = 478 - 475 100 / 100 = 0 . 3 , p -value = 0.38. Do not reject H 0 . (b) z * = 478 - 475 100 / 1000 = 0 . 95 , p -value = 0.17. Do not reject H 0 . (c) z * = 478 - 475 100 / 10000 = 3 , p -value = 0.001. Reject H 0 .

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Fall '09

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern