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# STATISTICAL METHODS STAT 303

Texas A&M

GPA 3.5

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This 8 page Class Notes was uploaded by Celestino Bergnaum on Wednesday October 21, 2015. The Class Notes belongs to STAT 303 at Texas A&M University taught by L. Longsine in Fall. Since its upload, it has received 14 views. For similar materials see /class/225755/stat-303-texas-a-m-university in Statistics at Texas A&M University.

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Date Created: 10/21/15

Suppose we have the following set of data 23 4 33 69 70 51 81 59 12 52 68 9 78 67 65 a Find the mean a and standard deviation s x add up the values 2343369705181591252689786765741 divide by the total number of observations 74115494 9 s subtract 3 from each of the observations square the difference and add them up 23494244942334942694942704942514942 81494259494212494252494268494294942 78494267494265494296836 divide by nl 96836146916857 take the square root W 263s b Find the ve number summary min median Q2 Q1 Q3 max and IQR median order the data from smallest to largest 4 9 12 23 33 51 52 59 65 67 68 69 70 78 81 the median is the nl239h value nl2l628 The 8Lh value is 4 9 12 23 33 51 52 2 65 67 68 69 70 78 81 so median59 Q1 take the rst half ofthe data 4 9 12 23 33 51 52 59 and nd the median nl245 So take the 43911 and 5Lh values and average them 2333228 Q1 Q3 take the second half ofthe data 59 65 67 68 69 70 78 81 and nd the median nl245 So take the 43911 and 5Lh values and average them 68692685 Q3 IQR subtract Q1 from Q3 6852840 51QR Also Min 4 and Max 81 0 determine ifthere are any outliers 15 IQR6075 Q1607528607532 75 Q 360 756856075129 25 Any value that is less than 3275 or greater than 12925 is an outlier Thus there are no outliers in this data set d Use the ve number summary to construct a boxplot Using the following data set 40 20 12 29 43 4 78 37 50 22 a Find the mean and standard deviation b Find the median and IQR 0 Compare the mean and median What can you infer about the distribution d Determine if there are any outliers Mean3ll standard deviation 2498 Median33 IQR23 MeanltMedian slightly left skewed 78 is an outlier Q3l5IQR 775 An athletic shoe company has designed a new type of running shoe and wants to see if it is marketable They take a random sample and ask people if they would buy the new running shoes Suppose the true proportion of people who would buy the shoes is TE 075 The above example has a binomial distribution where the probability of success is 075 We can apply the normal distribution to which of the following samples 1 1115 2 1130 3 n80 4 1140 We need nnE 10 and nl7I210 For n 15 nn 1125 and nl7I 375 For n 30 nn 225 and nl7I 75 For n 80 mt 60 and nl7I 20 For n 40 nn 30 and nl7I 10 Thus we can apply the normal distribution to the samples where n 40 and n 80 What is the sampling distribution for these two samples 2 2 7rl 7 7r 7525 4 T l 750T 1 2 2 P N M J N75 J N7504842 n 80 p N N7506852 ON YOUR OWN Suppose we have a binomial distribution with population proportion TE 048 We can apply the normal distribution to which of the following samples 5 n18 6 1125 7 n36 8 1120 For the samples you chose what are the sampling distributi0ns Answers Thus we can apply the normal distribution to the samples where n 25 and n 36 We have shown that as sample size n is increased the more normal our distribution turns out to be The sampling distributions for n 25 and n 36 are 2 2 P N N7r M J N48 w N4809992 n 25 2 2 P N N7r M N481 w N4808332 n 36 Suppose we have a sample of 58 people with a sample mean of 86 and we are given that o 33 It is believed that the population mean is 7 We want to try to show that the true mean is different from 7 using our sample We will use at 005 Specify the null hypothesis H0 u 7 Specify the alternative hypothesis Ha u i 7 86 7 Calculate the test stat1st1c z T 37 7 Compute the probability The alternative hypothesis is twosided so use ztable to nd 2PZ gt lzl 2PZ gt 2 2PZ gt 37 217 09999 00002 Should we reject H0 00002 lt 005 so we reject H0 ON YOUR OWN Suppose we have a sample of 21 people with a sample mean of 194 and we are given that o 67 It is believed that the population mean is 19 or less We want to try to show that the true mean is more than 19 using our sample We will use at 005 Specify the null hypothesis Specify the alternative hypothesis Calculate the test statistic Compute the probability Should we reject H0 ANSWERS Specify the null hypothesis H0 u S 19 Specify the alternative hypothesis Ha u gt 19 194 19 Calculate the test stat1st1c z T 027 M Compute the probability The alternative hypothesis is onesided and we are trying to show true mean is greater than 19 so use ztable to nd PZ gt z PZ gt z PZ gt 02717 06064 03936 Should we reject H0 03936 gt 005 so we fail to reject H0

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