Template.Reg.Hyp.Test.p.27K

Template.Reg.Hyp.Test.p.27K - Problem No RES Ramon Mo“...

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

View Full Document Right Arrow Icon
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problem No. RES Ramon Mo“ K (2'27) g-Besgi an EA“ da‘l’ac) Parametric Hyp thesis Testing Template (9.23.09) 1.a Identify the relevant given summary statistics and other information in the problem and summarize in terms of the usual statistical symbols: fit oLD Taniwsflérflékcd 5 0.8 2cm .HerlA A=l.3\5 n57 §%~:2;w_____ 1b.Identify and define the unknown parameter(s) and if several parameters, the possible parameter combination )8‘5 UNknoum pep. Slope. usuoj new training mail'lnod sh E($)=fi¢+6\gl"\! 1c.In terms of this parameter(s) (or parameter combination), what question are you being asked to answer when you conclude your hypothesis test? :5 5.7118 1d.Identify the = value in terms of the parameter(s) or parameter combination. 0:8 1e.Answer the question identified above if you believe the parameter or parameter combination are <, =, or > the equal value identified above, i.e. if you believe the parameter or parameter combination is <, =, > than the equal value identified above, you would answer the above identified question respectively either YES or NO. M: 0J0 < equal value ANS:_.ND_____ = equal value ANS:_\LQ$_.____ > equal value, ANS: Nb 1f.Set up the null and alternative hypotheses in terms of the parameter(s) (or parameter combination). H0 always includes the “=” value and any other values for which (4—39 you would take the same action as the — value. H0: £5. = ‘3 H05 é] = ‘8 E H]: é] '8 9 H11 5} '1: 'g ; NAME: 2.a What statistic would estimate the parameter (or parameter combination)? In the case of multiple parameters, give the ’ statistic typically used to test these hypotheses. 3. 2b. Find a distribution fact which is directly related to this statistic. Note that it will also typically contain the parameter or parameter combination. Write DF # and the DP. including distribution 3'35“ g I s A D.F. # 7 ;i.e., idimor 2c.From this distribution fact, give the test statistic and known distribution under the null hypothesis. Identify this test statistic with a brief identifier (like 20b5, tabs, xobs, F obs, etc.) which reminds you of the distribution under the null hypothesis. (In some cases, the test statistic and distribution under the null hypothesis are already given in the distribution fact above.) We typically derive the test statistic from the above distribution fact by substituting the “=” value of the unknown parameter for parameter combination) under the null hypothesis to get the test statistic taking care NOT to substitute for the estimate of the unknown parameter (or parameter combination. (In some cases, a distribution fact will actually be the test statistic in the next step.) sficgd-c W l; obs: (zingflnéz =nvfiowmea.) 5 A ‘6 under H0 ‘ '- 3.Look at the test statistic:(2c)@ ’ ) /' l (b 7- and (10le . Decide what extreme values of the test statistic would tend to indicate that H, is true (general direction). We do this in two steps when possible. 3a.Identify the estimate of the unknown parameter (or parameter combination) in the hypotheses (given typically in 2a above), and indicate what extreme values of this estimate would indicate the alternative hypothesis is true (general direction) Reject H0 if: J8. much SYQJ‘U ‘3)” ”GLEA less than 0 .% 3b.Use this information as it applies to the test statistic, and indicate what extreme values of the test statistic would indicate the alternative hypothesis is true (general direction) Reject H0 if: t- .obs VBI'Y 4305. 6? ~1er fitflaiul‘fi Problem No. (cont) Re)“ m M“ k Q12 7 3c.Drawra number line, label it under the right side *3 .obs, and shade and identify where you would Reject Ho Mf/ é/N l/lfi 45ch 4.Use the results of #2 and #3 along with the value of the probability of a type I error to find the cutoff point(s) for the acceptance and rejection region(s). Note or=Pr{Reject HOJHO true}.1N THE SPACE 4a—c below:a. To do this, we recopy the previous number line including the shaded parts of the axis, drawing and labeling the distribution of the test statistic under H0 above the number line. b. We then shade the areas under the curve above the shaded parts of the axes and label these areas above the curve in terms of CF, typically as or: or oc=/2. c. We label below the axes the border(s) between the shaded and unshaded regions in terms of X exit where “X” is the symbol we used when we wrote X obs above. Sometimes we will write -X cm and +X crit , and at other times we may use X cm, Lowe]. and X muppe, when we have multiple critical values. Complete 4d-4i below to find the critical values. 4d. If you do NOT have a Table for the distribution in la, convert the distribution picture in 4a—c to one in 4d for which you have a Table. [Example: 4a-c N(u,62) => 4d N(0,l) using z=(x—u)/6 ] 4a-c 4e. Symbo for unknown in 4a-c: b3 fi", is an area or score? 0 < £03, < 60 4g. Draw TP in 4g below. 4h. Put 4d (4a—c if no 4d) in terms of the TP in 4h below. Look up table values representing them as TP and get your answer in terms of the unknown. 4f.Bound on unknown: 4h (cont) 4h (cont) 4h. (cont) Final answer in terms of unknown in 4e: ‘20er 7" Z .O ‘5 4i. Check if final answer is consistent with bound in 4f. \/ 5.Clearly state your decision rules. It may be advantageous to NOT include the critical boundary points in the Accept Ho region and to list the Reject Ho region as “otherwise” AcceptHo l? ‘2.0|;< *0ia5< 2-0“; Reject Ho otherwise 6a. Calculate below your test statistic given in 20 using information in la. +0195: Q.3l’5-n8) mm 5 3.05 6b. Using the decision rules in #5, indicate whether you will Accept H0 or Reject Ho: Réflec} lib 6c. Interpret your results. (If you have transformed the problem, typically we interpret the results in terms of the original parameters.) Usmg a “3% laurel olT stSniiaccxme) 2*‘l‘énled l’tiotl'beB'ts 'lesstj we Conduéc $6 fl‘>.8 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern