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by: Newton Bradtke


Newton Bradtke
GPA 3.65

Lorrie Hoffman

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Lorrie Hoffman
Class Notes
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This 10 page Class Notes was uploaded by Newton Bradtke on Saturday October 3, 2015. The Class Notes belongs to MATH 2200 at Armstrong Atlantic State University taught by Lorrie Hoffman in Fall. Since its upload, it has received 30 views. For similar materials see /class/217865/math-2200-armstrong-atlantic-state-university in Mathematics (M) at Armstrong Atlantic State University.

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Date Created: 10/03/15
Con dence Intervals and Testing on Means What of continuous EX Instead of do you walkbike might be interested in how far you travel to campus The pertinent questions 0 How many should we sample We calculate 100 for a certain accuracy but no time to do it o What hypothesis test should we do 0 Build a con dence interval Using the Central Limit Theorem it assures us that sample means cluster in a bell about the population mean With Wiggle room of stdevsqrt of sample size With the continuous data we will use t Values instead ofzValues so 95 sure will no longer be 2 but something larger There is a tdistribution associated with every different sample size n We say that we have a t with dfdegrees of freedom equal to n 7 1 called v t is dashed normal is solid The ttables are found in the text Upper tail probability df 10 05 025 01 1 3078 6314 12706 31821 2 1886 2920 4303 9925 3 1638 2353 3182 4541 45 50 1299 1676 2009 2403 1000 1282 1645 1960 2326 80 90 95 98 Con dence level Must read differently than the Normal tables QConduct a hypothesis test with OL 05 to test whether H0 u 12 versus HA u lt12 commute miles to campus Step 1 see hypotheses above Step 2 what type of data will you collect Discrete binomial or continuous Since it is continuous I will be relying on the tdistribution I still want to answer whether the data s mean is far enough below my guess of 12 for me to say the campus average is lower and will do so by forming a zscore now called a tscore and seeing if it is a big negative value OR EQUIVALENTLY if the tscore s corresponding pValue is small compared to CL 05 Step 4 Is tscore from the data gt tvalue in table Then our data supports 12 Is tscore lt tvalue in table Then our data rejects 12 and we decide lt12 Extension of Step 4 Can we do pValues hard with ttables Note the pValue is sometimes a gross approximation from the t tables not as good as from the ztables Find an approximate pValue for your tscore from your data Is the pValue gt OL 05 then our data supports u12 Is the pValue lt OL 05 then our data rejects u12 and we decide ult12 Miles Miles Miles Miles Do you think Miles from campus follow a normal distribution Remember if the original data is normal then the tscore X usJH follows a tdistribution with df n 1 identi es the row in the ttable Go back and do the computations Now let s instead build a 90 confidence interval for the mean number of miles traveled to campus Recall that gt is about equal to p with a ruler Wiggle room of s n So 90 ofthe Q are within tgdfn12 sxH of u What value does t gdfn1 2 take Note C1 are always 2tailed in this class We have 114 We have X We have t gdfn1 2 We have s So we have sxH We can be 90 sure the population all AASUers travel between these miles to campus tdfn1 gtxlt SN Which is the proper conclusion 1 We are 90 sure that all AASUers travel between 2 90 of all AASUers travel this many miles to campus 3 We are 90 sure that a randomly selected AASUer will have traveled between miles to campus 4 The mean miles traveled to campus will be in 90 of the time 5 We are 90 sure that the mean number of miles traveled to campus by AASUers is in


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