L27HypothesisTesting_4

L27HypothesisTesting_4 - MGT 2250 — Lesson 27 Steps in...

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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: One-tail Upper (l-T-U), One—tail Lower (l—T-L) or Maj ” 3.) 4.) Two Tail (2-T) 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 \O "\lX 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 é Q a: a D? L (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 p-Values \ Note: We Will not determine p-Values for tests using the t-table 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 p-value 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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L27HypothesisTesting_4 - MGT 2250 — Lesson 27 Steps in...

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