Workshop 9 Solutions(2)

# Workshop 9 Solutions(2) - Workshop 9 Solutions THE...

This preview shows pages 1–4. Sign up to view the full content.

Workshop 9 Solutions T HE U NIVERSITY OF S YDNEY Q UANTITATIVE B USINESS A NALYSIS Prepared by: Scott Liu Workshop Aims 1. Understand the type of hypotheses that we test and how to select the null and alternative hypotheses. 2. Understand the difference between a one-tail test and a two-tail test. 3. Understand the types of errors we can make when we test hypotheses. 4. Use the 6 step procedure to undertake a hypothesis test for a mean. 5. Write a one sentence report (other than reject H 0 ) relating the conclusion back to the problem. 6. Calculate the p -value for a test statistic.

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

View Full Document
BUSS1020 Quantitative Business Analysis Workshop 9 Solutions Workshop 9 Question 1 For each of the following tests of hypotheses about μ , determine the rejection region if σ is known. (a) H 0 : μ = 100, H 1 : μ 6= 100, α = 0.05 (b) H 0 : μ = 50, H 1 : μ > 100, α = 0.01 (c) H 0 : μ = 15, H 1 : μ < 100, α = 0.1 Solution (a) This is a two-tailed hypothesis test with a 5% level of significance. Using NORM . INV ( 0 . 025 , 0 , 1 ): Reject if: | Z stat | > 1.96 (b) This is an upper-tail hypothesis test with a 1% level of significance. Using NORM . INV ( 0 . 01 , 0 , 1 ): Reject if: Z stat > 2.326 (c) This is a lower-tail hypothesis test with a 10% level of significance. Using NORM . INV ( 0 . 1 , 0 , 1 ): Reject if: Z stat < - 1.282 Note | Z stat | > 1.96 is the same as saying Z stat > 1.96 and Z stat < - 1.96. Question 2 For each of the following parts, determine the test statistic and rejection region. (a) H 0 : μ = 100, H 1 : μ 6= 100, α = 0.05, ¯ x = 90, s = 20, n = 40 (b) H 0 : μ = 50, H 1 : μ > 50, α = 0.01, ¯ x = 53, s = 10, n = 80 (c) H 0 : μ = 15, H 1 : μ < 15, α = 0.1, ¯ x = 13.5, s = 20, n = 240 Solution (a) This is a two-tailed hypothesis test with a 5% level of significance and degree of freedom 40 - 1 = 39. Using T . INV ( 0 . 025 , 39 ): Reject if: | t stat | > 2.023 (b) This is an upper-tail hypothesis test with a 1% level of significance and degree of freedom 80 - 1 = 79. Using T . INV ( 0 . 01 , 79 ): Reject if: t stat > 2.374 (c) This is a lower-tail hypothesis test with a 10% level of significance and degree of freedom 240 - 1 = 239. Using T . INV ( 0 . 1 , 239 ): Reject if: t stat < - 1.285 University of Sydney Page 2
BUSS1020 Quantitative Business Analysis Workshop 9 Solutions Question 3 For each of the following parts, state the null and alternative hypotheses. (a) The manager of the Danvers-Hinton Resort believes that the mean guest bill is more than \$500.00. (b) A long distance trucking firm believes that its mean weekly loss due to damaged shipments is less than \$2000. (c) An automobile assembly line operation has a scheduled mean completion time of 2.2 minutes. (d) Historically, long distance telephone calls from Sydney have averaged 15.20 minutes per call. (e) Gross Domestic Product has grown by less than 4% per year over the last 30 years. (f) The mean weekly rental fee for second-floor two-bedroom apartments in the city is more than \$400. (g) The mean family size in New South Wales is less than 4.3. Solution (a) H 0 : μ = 500, H 1 : μ > 500 (b) H 0 : μ = 2000, H 1 : μ < 2000 (c) H 0 : μ = 2.2, H 1 : μ 6= 2.2 (d) H 0 : μ = 15.20, H 1 : μ 6= 15.20 (e) H 0 : μ = 0.04, H 1 : μ < 0.04 (f) H 0 : μ = 400, H 1 : μ > 400 (g) H 0 : μ = 4.3, H 1 : μ < 4.3 Solution (1) The null hypothesis is always have the ‘=’ sign.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ 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