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Unformatted text preview: Problem No. RES Ramon Mo“ K (2'27) gBesgi 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.) sﬁcgdc 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 4d4i 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: 4ac N(u,62) => 4d N(0,l) using
z=(x—u)/6 ] 4ac 4e. Symbo for unknown in 4ac: 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< 20“; Reject Ho otherwise 6a. Calculate below your test statistic given in 20 using
information in la. +0195: Q.3l’5n8) 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 ...
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 Fall '10
 Szatrowski

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