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Unformatted text preview: MGT 2250 — Lesson 27
Steps in Hypothesis Testing All Types of Tests — Mean — Small Sample v
April 8, 2011 Example: The bad debt ratio for ﬁnancial institutions is deﬁned as the
dollar value of loans defaulted divided by the total dollar value of all
loans made and then expressed as a percentage. A random sample of
Ohio banks was selected and the bad debt ratios were as follows: 7% 4% 6% 7% 5% 4% 9% We: :7
Ohio banking officials claimed that the mean bad debt ratio for Ohio
banks was 3.5%, but one banking ofﬁcial believed it was really higher
than that. Assuming the population of bad debt ratios to be normally
distributed, but the population standard deviation to be unknown, run a hypothesis test to see if the average bad debt ratio was indeed hi her
than 3.5%. IQMDevelop and state the Null Hypothesis and the Alternative Hypothesis. H C} t, if“ ‘3: .3? , 5A
/ v as“,  ﬁ/‘K . / 3 ” ‘3 .i
2.) Check the flow diagram for appropriate statistics to use based
, on information available. What is the sample size? Is the \f population normally distributed? Do we know the population
standard deviation? ible
1. tr “Tee Li: Specify (set) the level of Signiﬁcance (alpha —OZ“‘% and
determine the rejection point. In this case, based on our
available information and the flow diagram, we need to use the
rejection point  trp — which we obtain from the t—table, based
on the alpha and the degrees of freedom (df). Note: (if: 11—]: dew“ Based on the hypotheses, determine the type of hypothesis test:
Onetail Upper (lTU), One—tail Lower (l—TL) or
Maj ” 3.) 4.) Two Tail (2T) PM ? Z,
61... L27HypothesisTesting#4 311.2,: K? H 1 5.) “Collect” the sample and determine the statistics needed.
We will need to do some calculating here! a.) n 2’7 b.), Sample Mean (3?? Eéﬁ22mé’Q c.) Sample Standard deviation (.5) '7‘ D.£(><h'£)1'
5W 2::_ l I "f; ‘1{ fl 9.2
o 0 5'7 ‘7, I i . \CE/JC’” 7
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wk K \ «——'—\ \m{%wvﬁ
,L L27HypothesisTesting#4 Using the Rejection Point Rule: 6.) Determine the rejection rule based on the rejection point — trp (This will be detern'EEd by alpha)
\Qﬁé T5 > {LP 2 W
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(L? /a%2(o 41/9732 CL? 7.) Calculate the test statistic  tts ,_ {833
«ED 2 i Q L ﬂ 5 #77
En. ,LCL Compare the test statistic — tts  with the rejection point  trp —
using the rejection rule. Q.) 2 ﬁg? (.9 L8? V55 rc\ 8.) 9.) Based on the rejection rule, decide hether’ you can reject H0 or not. @ Q/J LELB pValues \ Note: We Will not determine pValues for tests using the ttable due to
the difﬁculty of interpolating. These do exist however, and a computer
program will provide them. The rejection rule for p—Values remains the
same —— If the pvalue is less than alpha, you can reject the null
hypothesis L27HypothesisTesting#4 5L5 2‘éfg CS TO BE USED IN A HYPOTHESIS TEST ABOUT HUUKt 9.2.25 SUMMARY OF THE TEST STATISTI
A POPULATION MEAN ' Can 0 ;
be assumed
known? V the population
approximately _ Use thesample . standard deviation A
V s to estimate a Can a
be assumed _ /Use the sample
standard deviation
s to estimate 0 Increase the
sample size to
n 2 30
to conduct the \ hypomesistest h :\ \ \\ \ ,4" _ f” 1‘ DISTRIBUTION Area or
probability Entries in the tab1e give 1 values for an area or probability in the upper tail of
the 1 distribution. For example, With‘lO
degrees of freedom and a .05 area in the
upper tail, 1.05 = 1.812. Degrees 1 9< Area in Upper Tail of Freedom .10 ( .05 a
3.078 6.314
1.886 2.920
1.638 2.353
1.533 2.132
1.476 2.015
.440 .943 1: Q .415 13‘ 95 .397 .360
1.383 .833
10 .372 .312
11 .363 1.796
12 1.356 1.782
13 1.350 1.771
14 .345 .761
15 .341 .753
16 1.337 .746
17 .333 .740
18 1.330 .734
19 .328 .729
20 .325 1.725
21 1.323 .721
22 .321 1.717
23 .319 .714
24 .318 .711
25 1.316 1.708
26‘ .315 1.706
27 .314 .703
28 1.313 .701
29 1.311 .699
30 .310 1.697
40 1.303 .684
60 1.296 .671
120 1.289 .658
cc .2132 645 .025 . 12.706
4.303
3.182
2.776 2.571
2.447
2.365
2.306
2.262 2.228
2.201
2.179
2.160
2.145 2.131
2.120
2.110
2.101
2.093 2.086
2.080
2.074
2.069
2.064 2.060
2.056
2.052
2.048
2.045 2.042
2.021
2.000
1.980
1.960 3.162.. 63.657
9.925
5.841
4.604 4.032
3.703,)
3.49 3.355
3.250 3.169
3.106
3.055
3.012
2.977 2.947
2.921
2.898
2.878
2.861 2.845
2.831
2.819
2.807
2.797 2.787
2.779
2.771
2.763
2.756 2.750
2.704
2.660
2.617
2.576 ...
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 Summer '08
 Milne
 Statistics, Standard Deviation, Null hypothesis, Statistical hypothesis testing

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